+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 by gbeditor-2 (72,810 points)
reshown Jun 30, 2019 by developer

3 Answers

+2 votes
C is correct one
answered Jun 30, 2019 by (34,820 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 (16,750 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.