HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Examine whether the following statement pattern is a tautology, a contradiction or a contingency.

(~ q ∧ p) ∧ (p ∧ ~ p)

Examine whether the following statement pattern is a tautology, a contradiction or a contingency.

(p ∧ ~ q) → (~ p ∧ ~ q)

Examine whether the following statement pattern is a tautology, a contradiction or a contingency.

~ p → (p → ~ q)

Prove that the following statement pattern is a tautology.

(p ∧ q) → q

Prove that the following statement pattern is a tautology.

(p → q) ↔ (~ q → ~ p)

Prove that the following statement pattern is a tautology.

(~p ∧ ~q ) → (p → q)

Prove that the following statement pattern is a tautology.

(~ p ∨ ~ q) ↔ ~ (p ∧ q)

Prove that the following statement pattern is a contradiction.

(p ∨ q) ∧ (~p ∧ ~q)

Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ ~p

If p is any statement then (p ∨ ∼p) is a ______.

Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ (~p ∨ ~q)

Prove that the following statement pattern is a contradiction.

(p → q) ∧ (p ∧ ~ q)

Fill in the blanks :

Inverse of statement pattern p ↔ q is given by –––––––––.

Show that the following statement pattern is contingency.

(p∧~q) → (~p∧~q)

Show that the following statement pattern is contingency.

(p → q) ↔ (~ p ∨ q)

Show that the following statement pattern is contingency.

p ∧ [(p → ~ q) → q]

Show that the following statement pattern is contingency.

(p → q) ∧ (p → r)

Using the truth table, verify.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

Using the truth table, verify

p → (p → q) ≡ ~ q → (p → q)

Using the truth table, verify

~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q.