Using the truth table, prove the followi...

Using the truth table, prove the following logical equivalence :
` p hArr q -= (p ^^ q) vv(~p ^^~q)`.

Text Solution

Verified by Experts

The entries in (3) and (8) column are identical.
`:. " " p hArr q = (p ^^q) vv (~p^^~q).`

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Using truth table, prove the following logical equivalence (p^^q) rarr r -= p rarr (q rarr r)

Using truth tables, prove the following equivalences : (1) ~pvvq-=~(p^^q)to[~pvv(~pvvq)] (2) p""iffq-=(p^^q)vv(~p^^~q) (3) (p^^q)tor-=pto(qtor)

Knowledge Check

(p ^^ q) vv (~q ^^ p) -=

A

`q vv p`

B

`P`

C

`~q`

D

`p ^^ q`

p to q is logically equivalent to

A

`p ^^ ~ q`

B

` ~ p to ~ q`

C

` ( p vv ~ q)`

D

none of these

Which of the following is logically equivalent to ~[p to (p vv ~ q)] ?

A

`p vv (~ p ^^ q)`

B

`p ^^( ~p ^^ q)`

C

`p ^^ (p vv ~q)`

D

`p vv (p ^^ ~q)`

Similar Questions

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

Which of the following is logically equivalent to ~[ p to ( p vv ~q)] ?

p ^^ (q vv r) -= (p ^^ q) vv (p ^^ r) is :

The logically equivalent statement of (p ^^ q) vv ( p ^^r) is

~p ^^ q is logically equivalent to

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