1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Choose the correct option. Statement 1:(p ∧∼ q)∧(∼ p∧q) is a fallacy. Statement 2:(p⇒q)⇔(∼ q⇒∼ p) is a tautology.

A
Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
STATEMENT 1 is FALSE and STATEMENT 2 is TRUE.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## If a logical compound statement always produces the truth (true value), then it is called a tautology.The opposite of tautology is called fallacy or contradiction, in which the compound statement is always false.Statement 1: (p ∧∼ q)∧(∼ p∧q) Using Set Theory approach, this can be expressed as: (P∩Qc)∩(Pc∩Q) Clearly, the resultant is ϕ. Hence, statement 1 is a fallacy. Statement 2:(p⇒q)⇔(∼ q⇒∼ p) Clearly, (∼ q⇒∼ p) is a contra-positive of (p⇒q) and vice-versa. Hence, statement 2 is a tautology.Hence, the correct option is C Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
4 Sides and 1 Diagonal
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program