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The only statement among the following i...

The only statement among the following i.e. a tautology is

A

` A vv ( A vv B)`

B

` [ A ^^ ( A to B)]toB`

C

` B to [ A ^^ ( A to B)]`

D

`A ^^ ( A vv B)`

Text Solution

Verified by Experts

The correct Answer is:
B
` A vv ( A vv B) = A and A ^^ ( A vv B) =A`
So , these two are not tautologies.
we know that ` A to B cong ~ A vv B`
` therefore A ^^ ( A to B) cong A ^^ ( ~ A vv B cong ( ~ A vv B cong ( A ^^ ~ A) vv ( A ^^ B) cong A ^^ B `
` Rightarrow [ A ^^ ( A to B) ] to B cong ( A ^^ B) to B cong ~ ( A ^^ B) vv B `
` cong ( ~ A vv ~ B) vv B cong U`
Hence, ` [ A ^^ ( A to B)] to B` is a tautology.
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