wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If the truth value of the statement p(qr) is false (F), then the truth values of the statements p, q, r are respectively :

A
T, F, F
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
T, F, T
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
F, T, T
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
T, T, F
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D T, T, F
Given p(qr) is false.
Option A) If p=T, q=T, r=F
so, T(T F)T(FF)TF
which is equal to F

Option B) If p=T, q=F, r=T
so, T(F T)T(TF)TT
which is equal to T

Option C) If p=F, q=T, r=T
so, F(T T)F(FT)TT
which is equal to T

Option D) If p=F, q=T, r=T
so, F(T T)F(FT)FT
is equal to T

Alternate solution:
xy is F only when x is T and y is F.
p(qr) is false only when P is T and (qr) is F, which is possible only when both q and r are F.
So, q is T and r is F.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon