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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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