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The logical statement [~(~pvvq)vv(p^^r)]...

The logical statement `[~(~pvvq)vv(p^^r)]^^(~q^^r)` is equivalent to (a) `(~p^^~q)^^r` (b) `~p vv r` (c) `(p^^r)^^~q` (d) `(p^^~q)vvr`

A

` (p wedge r) wedge ~q`

B

`(~p wedge ~q)wedge r`

C

`~p vee r`

D

`(p wedge~q)vee r`

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The correct Answer is:
A
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~(pvvq)vv(~p^^q) is equivalent to

For any two statements p and q, ~(pvvq)vv(~p^^q) is logically equivalents to

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

Construct the truth table for the followings statements : (a) (p^^q) to ~ p " " (b) (p^^q) to (pvvq) (c) (p^^q) to r " " (d) [p^^(~r)] to (qvvr)

Show that the compound statements (pvvq)^^~p and ~ p^^q are logically equivalent.

Show that ~(p harr q) -= ( p ^^ ~q) vv(~p ^^q) .

Find the truth values of (a) (pharr~q) harr(p to p) " " (b) (p to q) vv~(p harr ~q)

Find the truth values of the following compound statements : (i) P^^(q^^r) " " (ii) (pvvq) vvr (iii) p^^(qvvr) " " (iv) (p^^q)vvr

Show that (pvvq) to r -= (p to r) ^^ (q to r)

If S(p,q,r)=(~p)vv[~(q^^r)] is a compound statement, then S(~p,~q,~r) is

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