Logic Question Calculate truth tables for the following sent

Logic Question:
Calculate truth tables for the following sentence: (A (B ¬B)) ¬A

Solution

we need to find the truth table for given senetence

(A (B ¬B)) ¬A

First find the truth table for some basic statement as below:

A B is a condition

A conditional is false only when the antecedent is true and the consequent is false

A B : conjuction

True only when both A and B is true

our statemnet is (A (B ¬B)) ¬A

Means it is false only when  (A (B ¬B)) is true and ¬A is false

where,

(A (B ¬B)) is false only when A is true and B ¬B is false

where,

B ¬B is true only when B and ¬B is true which is never possible as ¬B is complement of B

Find the trurth table for our statement as below: