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Q.No. 1 Solution:
P = The number is divisible by 12
~P = The number is not divisible by 12
q= The number is divisible by 3 and 4.
~q = The number is not divisible by 3 and 4.
Meanings Symbols Called
not ~ Tilde
if and only if ↔ Double arrow
Therefore ∨ Vel
p q ~P ~q ~P↔~q P ∨ q
T T F F T T
T F F T F T
F T T F F T
F F T T T F
Test the truth table is valid or invalid:
An argument is valid if the conclusion is true when all the premises are true.
An argument is invalid if the conclusion is false when all the premises are true.
Premises Premises Premises conclusion
~P↔~q P ∨ q p q
T T T T
F T T F
F T F T
T F F F
← Critical Row
In the First critical row, the conclusion is True when the premises ~P↔~q, P ∨ q , p are true. Therefore, the argument is valid.
Q. No.2 Solution:
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