EXERCISE . . Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing each of the following statements.
(i) ¬ p (ii) p ∧¬ (iii) ¬ ∨ (iv) p →¬ (v) p ↔ . Write each of the following sentences in symbolic form using statement variables p and q . (i) is not a prime number and all the angles of a triangle are equal. (ii) is a prime number or all the angles of a triangle are not equal (iii) is a prime number and all the angles of a triangle are equal (iv) is not a prime number .
Determine the truth value of each of the following statements (i) If , then the milk is white. (ii) China is in Europe or is an integer (iii) It is not true that or Earth is a planet (iv) is a prime number and all the sides of a rectangle are equal . Which one of the following sentences is a proposition? (i) (ii) What are you doing?
(iii) (iv) Peacock is our national bird (v) How tall this mountain is! . Write the converse, inverse, and contrapositive of each of the following implication. (i) If x and y are numbers such that x , then x (ii) If a quadrilateral is a square then it is a rectangle .
Construct the truth table for the following statements. (i) ¬ ∧¬ (ii) ¬ ∧¬ (iii) ( ∨¬ (iv) ( ¬ → ↔ Discrete Mathematics . Verify whether the following compound propositions are tautologies or contradictions or contingency (i) ( ∧¬ (ii) ( ∧¬ ) → (iii) ( ↔¬ → (iv) ( ) → . Show that (i) ¬ ≡¬ ∨¬ q (ii) ¬ ≡ ∧¬ q .
. Prove that q ≡¬ →¬ . Show that p ® and q ® are not equivalent . Show that