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Explanation on If and only if statement:
The bi-conditional truth table results in a true compound proposition if , and only if, both propositions are either true or false. If one proposition is true while the other is false, the compound proposition is false.
Explanation on If statement:
If the premises is false or the two propositions are true, then the compound statement is True. But, if the first proposition is true, while the other is false. Then the compound statement is False
1. 1+1=3 is false and also, 2+2=3 is also false. Therefore the compound statement is True
2. 1+1=2 or 1+1=3 is true, also 2+2=3 and 2+2=4 is false. Therefore the compound statement is False
3. Squirrel plays badminton is false, also cat can't fly is true. Therefore the compound statement is True