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If the truth value of the statement p to...

If the truth value of the statement `p to (~q vee r)` is false (F), then the truth values of the statements p,q and r are respectively

A

T, T and F

B

T, F and F

C

T, F and T

D

F, T and T

Text Solution

Verified by Experts

The correct Answer is:
A
Key idea Use formula:
`P to q = ~ p vee q`
Given statement is
`p to (~ q vee r)= ~ p vee (~ q vee r)`
Now, from the options
(a) When `p = T, q = T and r = F`
then `~ p vee ( ~ q vee r) = F vee (F vee F) = F`
(b) When `p = T, q = F and r = F`
then ` ~ p vee ( ~ q vee r)=F vee (T vee F) = T`
(c ) When `p = T, q = F and r = T`
then `~ p vee ( ~ q vee r) = F vee (T vee T) =T`
(d) When `p = F, q = T and r = T`
then `~ p vee ( ~ q vee r) = T vee (F vee T)=T`
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