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The negation of ~svv(~r^^s) is equivale...

The negation of `~svv(~r^^s) ` is equivalent to

A

`a wedge r`

B

`~ a wedge ~ r`

C

`s vee r`

D

r

Text Solution

Verified by Experts

The correct Answer is:
A
Key Idea Use De-morgan's law, Distributive law and Identity law as `p vee F -= p`
The given boolean expression is ` ~ s v ((~ r ) wedge s)`
Now, the negation of given boolean expression is
` ~ (~ x vee (( ~ r ) wedge s))`
`= s wedge ( ~((~r) wedge s)) " " [ because ~ (p wedge q)= ~ p vee ~q]`
`=s wedge (r vee ( ~ s)) " "[ because ~ (p vee q)= ~ p wedge ~ q]`
`=(s wedge r) vee (s wedge ( ~s)) " " [ because p wedge (q vee r) = (p wedge q) vee ( p wedge r)]`
`=(s wedge r) " " [ because p wedge ~ p -= F]`
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