Exercise 1.4 (4)

Assuming that the following statements are true,
p : Sunday is holiday,
q : Ram does not study on holiday,
find the truth values of the following statements.
i) Sunday is not holiday or Ram studies on holiday.
ii) If Sunday is not holiday then Ram studies on holiday.
iii) Sunday is a holiday and Ram studies on holiday.
Ans:
i) Symbolic form of the given statement is ~p∨~q.
∴ ~p∨~q  ≡ ~T∨~T
                 ≡ F∨F
                 ≡ F 
Hence, truth value is F.

ii) Symbolic form of the given statement is ~ p→~q.
∴ ~p→~q ≡ ~T→~T
                   ≡ F→F
                   ≡ T
Hence, truth value is T.

iii) Symbolic form of the given statement is p∧~q.
∴ p∧~q ≡ T∧~T
              ≡ T∧F
              ≡ F
Hence, truth value is F.