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The logical statement [~(~pvee q) vee (p...

The logical statement `[~(~pvee q) vee (p vee r) wedge (~q wedge r)]` is equivalent to

A

`~p vee r`

B

`(p wedge ~q) vee r`

C

`(p wedge r) wedge ~q`

D

`(~p wedge ~q)wedge r`

Text Solution

Verified by Experts

The correct Answer is:
C
Clearly, `[~(~p vee q) vee (p wedge r)] wedge (~q wedge r)`
`-= [(p wedge ~q) vee (p wedge r)] wedge (~q wedge r)`
(`because ~ (~p vee q) -= ~ (~p) wedge ~q -= p wedge ~q ` by De Morgan's law)
`-=[p wedge (~q vee r)] wedge (~q wedge r)] " " `(distributive law)
`-= p wedge [(~q vee r) wedge (~q wedge r)] " " ` (associative law)
`-= p wedge [(~q wedge r) wedge (~q vee r)] " " ` (commutative law)
`-= p wedge [{(~q wedge r) wedge (~q)} wedge {(~q wedge r) wedge r]` (distributive law)
`-= p wedge [(~ q wedge r) vee (~q wedge r)] " " `(idempotent law)
`-= p wedge [~q wedge r] " " ` (idempotent law)
`-= p wedge ~q wedge r-= (p wedge r) wedge (~q) " " `(associative law)
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