{"id":19729,"date":"2020-01-14T09:51:49","date_gmt":"2020-01-14T04:21:49","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=19729"},"modified":"2021-07-02T15:29:38","modified_gmt":"2021-07-02T09:59:38","slug":"2nd-puc-basic-maths-question-bank-chapter-6-ex-6-2","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-question-bank-chapter-6-ex-6-2\/","title":{"rendered":"2nd PUC Basic Maths Question Bank Chapter 6 Mathematical Logic Ex 6.2"},"content":{"rendered":"

Students can Download Basic Maths Exercise 6.2 Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers<\/a> helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka 2nd PUC Basic Maths Question Bank Chapter 6 Mathematical Logic Ex 6.2<\/h2>\n

Part – A<\/span><\/p>\n

2nd PUC Basic Maths Mathematical Logic Ex 6.2 One Mark Questions and Answers<\/strong><\/p>\n

Question 1.
\nNegate the following propositions.
\n(1) p \u2228 ~ q
\n(ii) ~p \u2192 q
\n(iii) ~p \u2227 ~q
\n(iv) p \u2227 ~q
\n(v) ~p \u2192 ~q
\nAnswers:
\n(i) ~ (p \u2228~q)\u00a0 \u2261 ~p \u2227~(~9) = ~p \u2227 q ( \u2235 ~(~q) = q )
\n(ii) ~(~p \u2192 q) \u2261 ~p \u2227 ~q
\n(iii) ~(~p \u2227~q) \u2261 ~(~p) \u2228~(~q) = p \u2228 q\u00a0 \u00a0(\u2235 ~(~p) = p)
\n(iv) ~ (p \u2227 ~q) \u2261 ~p \u2228~(~q) = ~p \u2228 q
\n(v) ~(~p \u2192~q) \u2261~p \u2227~(~q) =~p \u2227 q.<\/p>\n

\"KSEEB<\/p>\n

Question 2.
\nNegate the following.
\n(i) 4 is an even integer or 7 is a prime number.
\n(ii) He likes to run and he does not like to sit.
\n(iii) He likes Mathematics and he does not like Logic.
\n(iv) If 6 is a divisor of 120 then 486 is not dividiable by 6.
\n(v) If 2 triangles are similar then their ares are equal.
\n(vi) It is cold or it is raining,
\nAnswers:
\n(i) Let p: 4 is even integer, q: 7 is a prime number given (p v q)
\n~(p \u2228 q) = ~ p \u2227 ~q
\n4 is not an even integer & 7 is not a prime number<\/p>\n

(ii) Let p: He likes to run, q: He likes to sit
\nGiven is ~ p \u2227 ~q
\n\u2234 ~ (p \u2227~ ) = ~p \u2228 ~(~q) \u2261 ~p \u2228 q
\nHe does not like to run or he likes to sit<\/p>\n

(iii) Let p: He likes mathematices, q: He like logic
\nGiven (p \u2227 ~q)
\n~ (p \u2227 ~q) \u2261 ~p \u2228 q
\nHe does not like mathematics or he likes logic<\/p>\n

(iv) Let p: 6 is a divisor or 120
\nq: 486 is divisible by 6
\nGiven (p \u2192 ~ q)
\n~(p \u2192 ~ q) = p \u2227 ~(~q)<\/p>\n

(v) Let p: 2 triangles are similar.
\nq: Areas are equal
\nGiven (p \u2192 q)
\n\u2234 ~(p \u2192 q) = (p \u2227 ~q)
\n2 triangles are similar & areas are not equal.<\/p>\n

(vi) p: It is cold
\nq: It is raining Given p \u2228 a
\n~(p \u2228 q) =~p\u2227~q
\nIt is not cold & it is not raining<\/p>\n

\"KSEEB<\/p>\n

Part B<\/span><\/p>\n

2nd PUC Basic Maths Mathematical Logic Ex 6.2 Two Marks Questions and Answers<\/strong><\/p>\n

Question 1.
\nNegate
\n(i) p \u2192 (q \u2227 r)
\n(ii) q \u2228 [~(p \u2227 r)] |
\n(iii) (p \u2192 q)\u2227( q \u2192 p\/q)
\n(iv) p\u2192 (q \u2227 ~r)
\nAnswers:
\n(i) ~ [p \u2192 (p \u2227 r)] = p \u2227~(q \u2227 r) \u2261 p \u2227 (~q \u2228 ~r)
\n(ii) ~ [q \u2228 (~ (p \u2227 r)] \u2261 ~q \u2227 ~[~ (p \u2227 r) \u2261 ~q \u2227 (p \u2227 r)
\n(iii) ~[(p \u2192q) \u2227 (q \u2192 p)] \u2261 ~ (p \u2192q) \u2228 ~(q \u2192 p)
\n\u2261 (p \u2227 ~q) \u2228 (q \u2227 ~p)
\n(iv) ~[p \u2192 (q^~r)] = p \u2227 ~(q \u2227 ~r)
\n= p \u2227 [(-q \u2228 ~(~r)]
\n= p \u2227(~q \u2228 r)<\/p>\n

\"KSEEB<\/p>\n

Question 2.
\nNegate the following:
\n(1) If an integer is greater than 3 and less than 5 then it is a multiple of 5.
\n(ii) If ‘x’ is divisible by ‘y’ then it is divisible by ‘a’ and ‘b.
\n(iii) Weather is fine and my friends are not coming or we do not go to a movie.
\n(iv) If a triangle is equilateral then it’s sides are equal and angles are equal.
\n(v) 14 is a divisor of 48 and 28 is not divisible by 82.
\nAnswers:
\n(i) Let p: An integer is greater than 3
\nq: An integer is less than 5
\nr: An integer is multiple of 5
\nGiven[(p \u2227 q) \u2192 r]
\n\u2234 ~ ((p \u2227 q) \u2192 r] = (p \u2227 q) \u2227~r
\nAn integer greater than 3 and less than 5 and not divisible by b<\/p>\n

(ii) Let P:x is divisible by y
\nq: x is divisible by a
\nr: x is divisible by b
\nGiven [p \u2192 (q \u2227 r)]
\n\u2234 ~P (q \u2227 r)] = p \u2227~(q \u2227 ~r)
\n= p \u2227( ~ ( q \u2228 ~r)
\nx is divisible by y and x is not divisible by a or not a multiple of 5<\/p>\n

(iii) Let p: Weather is fine
\nq: Friends are coming
\nr: we go to a movie
\nGiven[p\u2227~q \u2228~r)]
\n~(p \u2227 (~q \u2228 ~r)) \u2261 ~p \u2228 ~(~ q \u2228 ~r) :
\n\u2261 ~p \u2228 (q \u2227 r)<\/p>\n

(iv) Let p = a triangle is equilateral
\nq: Sides are equal
\nr: angles are equal
\nGiven p \u2192 (q \u2227 r)
\n\u2234 ~(p \u2192 (~q \u2228 ~r)) \u2261 ~p \u2227 ~q \u2228 ~r)
\nA triangle is equilateral and sides are not.
\nequal or angles are not equal.
\nLet p: 14 is a divisor of 48
\nq: 28 is divisible by 82
\nGiven p \u2227 ~q
\n\u2234\u00a0 ~(p \u2227 ~q) \u2261 ~p \u2228 q
\n14 is not a divisor of 48 or 28 is divisible by 82<\/p>\n

\"KSEEB<\/p>\n

Question 3.
\nDetermine whether the following propositions is a Tautology or a contradiction or neither.
\n(i) (p \u2227 q) \u2227 ~p
\n(ii) [~p \u2227 (p \u2228 q)]
\n(iii) (p \u2227 q) \u2192 (p \u2228 q)
\n(iv) (p \u2227 q) \u2192p
\n(v) ~ p \u2227 ~q
\nAnswers:
\n(i) (p \u2227 q) \u2227~p
\n\"2nd
\nFrom last column we conculde that it is a contradiction<\/p>\n

(ii) [~p \u2227 (p \u2228 q)]
\n\"2nd
\nFrom last column we conclude it is neither tautology nor a contradiction<\/p>\n

(iii) (p \u2227 q) \u2192 (p \u2228 q)
\n\"2nd
\nFrom last column we conclude it is a tautology<\/p>\n

(iv) (p \u2227 q) \u2192 p
\n\"2nd
\nFrom last column we conclude that it is a tautology<\/p>\n

\"KSEEB<\/p>\n

(v) ~ p \u2227 ~q
\n\"2nd
\nIt is neither tautology nor contradiction<\/p>\n

Part C<\/span><\/p>\n

2nd PUC Basic Maths Mathematical Logic Ex 6.2 Five Marks Questions and Answers<\/strong><\/p>\n

Question 1.
\nCheck whether the following propositions is a Tautology or a contradiction.
\n(i) (p \u2227 ~q) \u2192 (p \u2227 q)
\n(ii) [~p \u2227 (p \u2228 q)] \u2192 q
\n(iii) (p \u2192q) \u2194 (~p \u2192~q)
\n(iv) [~(p \u2192~q)] \u2228 (~ p \u2194 q)
\n(v) (~p \u2228 q) \u2194 (p \u2228~9)
\nAnswers:
\n(i) (p \u2227~q) \u2192 (p\u2227q)
\n\"2nd
\nIt is neither Tauthology nor contradiction<\/p>\n

(ii) [~p \u2227 (p \u2228 q)] \u2192 q
\n\"2nd
\nF From last column we conclude it is a tautology<\/p>\n

(iii) (p \u2192q) \u2194 (~p \u2192~q)
\n\"2nd
\nF It is neither a tautology nor contradiction<\/p>\n

(iv) [~(p \u2192~q)] \u2228 (~ p \u2194 q)
\n\"2nd
\nIt is neither tautology nor contradiction<\/p>\n

(v) (~p \u2228 q) \u2194 (p \u2228~9)
\n\"2nd
\nIt is neither tautology nor contradiction<\/p>\n

Question 2.
\nShow that (p \u2192 q) + (~q\u2192~p) is a Tautology.
\nAnswer:
\n\"2nd
\nIt is a tautology<\/p>\n

\"KSEEB<\/p>\n

Question 3.
\nShow that ~(p \u2228 q) \u2192(~p\u2227~q) is a Tautology.
\nAnswer:
\n\"2nd
\nIt is a tautology<\/p>\n

Question 4.
\nProve : [(p \u2192q) \u2227 (q \u2192r)] \u2192 (P\u2192r) is a Tautology.
\nAnswer:
\n\"2nd
\nFrom last column we conclude that it is a tautology<\/p>\n

Question 5.
\nProve that (p \u2228 q) \u2227 (~p \u2227~q) is a contradiction.
\nAnswer:
\n\"2nd
\nFrom last column we conculde that it is a contradiction<\/p>\n

\"KSEEB<\/p>\n

Question 6.
\nShow that [(~p ^ q) ^ (q ^ r) ^ (~q)] is a contradiction.
\nAnswer:
\n\"2nd
\nFrom last column we conclude that it is a contradiction<\/p>\n

Question 7.
\nExamine whether the following are logically equivalent:
\n(i) p \u2194 q and (p \u2192 q) \u2227 (q \u2192 p)
\n(ii) p \u2192 (q \u2192 r) and (p \u2192 q) \u2192 r
\n(iii) (p \u2227 ~q) \u2228 q and p \u2228 q.
\n(iv) p \u2194 q and (~ p \u2228 q) \u2227 (~q \u2228 p)
\n(v) p \u2227 q and ~(p \u2192~q)
\n(vi) ~ (p \u2194 q ) and (p \u2227 ~q) \u2228 (q \u2227~p)
\n(vii) p\u2228 (q \u2227 r) and (p \u2228 q) \u2227 (p \u2228 r)<\/p>\n

(i)
\n\"2nd
\nFrom 3rd & 6th column we conclude that
\np \u2194 q (p \u2194 q) \u2227 (q \u2194 p)<\/p>\n

(ii) p \u2192 (q \u2192 r) and (p \u2192 q) \u2192 r
\n\"2nd
\nFrom last two columns we conclude that p \u2192 (q \u2192 r) and (p \u2192 q) \u2192 r are not logically equivalent<\/p>\n

(iii) (p \u2227 ~q) \u2228 q and p \u2228 q.
\n\"2nd
\nFrom last two columns we conclude (p \u2227 ~q) \u2228 q p \u2228 q.<\/p>\n

(iv) p\u2194 q and (~ p \u2228 q) \u2227 ( ~q \u2228 p)
\n\"2nd
\nFrom 3 rd and 8 th columns we conclude that p \u2194 q \u2261 (~ p \u2228 q) \u2227 (~q \u2228 p)<\/p>\n

(v) P \u2227 q and (p \u2192 ~q)
\n\"2nd
\nColumn 3 and column 6 are identical :
\n\u2234 They are logically equivalent<\/p>\n

(vi) ~ (p \u2194 q ) and (p \u2227 ~q) \u2228 (q \u2227~p)
\n\"2nd<\/p>\n

4th<\/sup> & th<\/sup> columns are identical \u2234 they are logically equivalent<\/p>\n

\"KSEEB<\/p>\n

(vii) p \u2228 (q \u2227 r) and (p \u2228 q)\u2227 (p \u2228 r)
\n\"2nd<\/p>\n

5th<\/sup> column & 8th<\/sup> columns are identical
\n\u2234 p\u2228 (q\u2227r) = (p \u2228 q)\u2227 (p \u2228 r)<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Basic Maths Exercise 6.2 Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 2nd PUC Basic Maths Question Bank Chapter 6 Mathematical Logic Ex 6.2 Part – A 2nd PUC …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[82],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/19729"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=19729"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/19729\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=19729"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=19729"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=19729"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}