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Statements -1 : ~(pharr~q) is equivalent...

Statements -1 : `~(pharr~q)` is equivalent to `p harr q`
Statement-2: `~( p harr ~q)` is a tautology.

A

Statement-1 is true, statement 2 is true, statement 2 is a correct explanation for statement 1

B

Statement 1 is true, statement-2 is true, statement 2 is not a correct explanation for statement 1

C

Statement 1 is true , statement 2 is false,

D

statement 1 is false, statement 2 is true

Text Solution

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The correct Answer is:
C
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Statements (p to q) harr (q to p)

Prove that the statement - ~(pharr q) harr {(p^^~q) vv (~p^^q)} is a tautology.

Knowledge Check

  • The statement ~(pharr~q) is -

    A
    equivalent to `pharrq`
    B
    equivalent to `~p harrrq`
    C
    a tautology
    D
    a fallacy

  • The statement ~(pharr~q) is

    A
    a tautology
    B
    a fallacy
    C
    equivalent to `pharrq`
    D
    equivalent to ~pharrq

  • consider : Statement - I : (p^^~q)^^(~p^^q) is a fallacy . Statement -II : (prarrq)harr(~qrarr~p) is a tautology .

    A
    Statement -I is true , Statement -II is true , Statement -II is a correct explantion for Statement - I .
    B
    Statement - I is true , Statement - II is true , Statement -II is not a correct explanation for Statement -I .
    C
    Statement - I is true , Statement -II is false .
    D
    Statement - I is false , Statement -II is true .

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    The proposition p to ~ (p^^~ q) is equivalent to

    Show that (p^^q)vv(~p)vv(p^^~q) is a tautology

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    Statement I : (p^^∼q)∧(∼p^^q) is a fallacy. Statement II : (p→q)↔(∼q→∼p) is a tautology.

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