+2 votes

S_1: \forall _x(P(x)\rightarrow A) \equiv \exists_x P(x) \rightarrow A

S_2: \exists _x(P(x)\rightarrow A) \equiv \forall_x P(x) \rightarrow A

Which of the following statements is true?

(A) Only S1

(B) Only S2

(C) Both S1 and S2

(D) Neither S1 not S2

asked Jun 28, 2019 in Discrete Maths by gbeditor (66,750 points)
reshown Jun 30, 2019 by getgatebook

3 Answers

+2 votes
C is correct one
answered Jun 30, 2019 by (34,780 points)
edited Jun 30, 2019 by
could someone tell me when the rank list for this test will be released ?
don't know man many of the answers are wrong
@tsvikasthamke2095 in couple of days
I think 11 wrong other than 11 all are now correct.
Or topper list may be released tomorrow before next test.
Is all the questions of DM uploaded? I am able to see only 15th question.
@tskushagra-guptacse , yes all DM questions are uploaded.
Yes. I found it. They should upload in the recent section.
Click on discreet mathematics
Now all questions are updated
+16 votes

\\ \forall x(P(x)\rightarrow A)=\exists xP(x)\rightarrow A\\ (P1\rightarrow A).(P2\rightarrow A)=(P1+P2)\rightarrow A\\ (P1'+A).(P2'+A)=(P1+P2)'+A\\ P1'P2'+A=P1'P2'+A\\ \\ \exists x(P(x)\rightarrow A )=\forall x P(x)\rightarrow A\\ (P1\rightarrow A)+(P2\rightarrow A)=P1P2\rightarrow A\\ (P1'+A)+(P2'+A)=(P1P2)'+A\\ P1'+P2'+A=P1'+P2'+A\\

Therefore ans should be C


answered Jun 30, 2019 by (16,710 points)
you are correct bhai ,I have made mistake in this question
You r correct bro.
In the first one, shouldn't there be a term (P1' + P2')A? Where did that go?
I have given the final result.
Do like this: P1'P2'+P1'A+P2'A+A  
+1 vote
C is the answer
answered Jul 1, 2019 by (870 points)
For problem 11
@tsnikhilsharmagate2018 none of these both are satisfiable.