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

Which of the following is a tautology from the given options?


A

pqqp

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

~ppqq

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

qp~pq

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

~qpqq

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

~ppqq


The explanation for the correct option:

The truth table of pq:

pqpq
TTT
TFT
FTT
FFF

The truth table of pq:

pqpq
TTT
TFF
FTF
FFF

Truth table of ~p

p~p
TF
FT

A tautology is a compound statement in Maths that always results in a Truth value.

It doesn’t matter what the individual part consists of, the result in tautology is always true.

The possible truth table of ~ppqq:

pq~ppq~ppq~ppqq
TTFTFT
TFFTFT
FTTTTT
FFTFFT

All outputs of ~ppqq are true.

So, it is a tautology.

Hence, the correct option is B)~ppqq.

The explanation for the incorrect options:

Truth table for pq

pqpq
TTT
TFF
FTT
FFT

The truth table of pqqp:

pqpqqppqqp
TTTTT
TFFTF
FTTFF
FFTTT

All outputs of pqqp are not true.

So, it is not a tautology.

Hence, the option A) is incorrect.

The truth table of qp~pq:

pqpqqp~pqqp~pq
TTTTFT
TFFTTT
FTTFFF
FFTTFT

All outputs of qp~pq are not true.

So, it is not a tautology.

Hence, the option C) is incorrect.

The truth table of ~qpqq:

pq~qpq~qpq~qpqq
TTFTTT
TFTFTF
FTFFFT
FFTFTF

All outputs of ~qpqq are not true.

So, it is not a tautology.

Hence, the option D) is incorrect.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Solving Inequalities
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon