Without using truth table prove that: p ∨ q ∧ p ∨ ~ q ≡ p

Use algebra of statements to prove that p ∨ q ∧ p ∨ ~ q ≡ p . So take LHS of the statement, p ∨ q ∧ p ∨ ~ q ≡ p ∨ q ∧ ~ q (Distributive Law) ≡ p ∨ F (Complement Law) ≡ p (Identity law) Hence Proved.

Without using truth table prove that: p ∧ q ∨ ~ p ∧ q ∨ p ∧ ~ q ≡ p ∨ q

Use algebra of statements to prove that p ∧ q ∨ ~ p ∧ q ∨ p ∧ ~ q ≡ p ∨ q . So take LHS of the statement, p ∧ q ∨ ~ p ∧ q ∨ p ∧ ~ q ≡ p ∨ ~ p ∧ q ∨ p ∧ ~ q (Distributive Law) ≡ T ∧ q ∨ p ∧ ~ q (Complement Law) ≡ q ∨ p ∧ ~ q (Identity law) ≡ q ∨ p ∧ q ∨ ~ q (Distributive Law) ≡ q ∨ p ∧ T (Complement Law) ≡ p ∨ q (Identity Law) Hence Proved.

Without using truth table prove that: ~ p ∨ ~ q → p ∧ ~ q ≡ p ∨ ~ q ∧ ~ p ∨ q

Use algebra of statements to prove that ~ p ∨ ~ q → p ∧ ~ q ≡ p ∨ ~ q ∧ ~ p ∨ q . So take LHS of the statement, Recall that ~ p → q ≡ p ∧ ~ q ~ p ∨ ~ q → p ∧ ~ q ≡ p ∨ ~ q ∧ ~ p ∧ ~ q (Conditional Law) ≡ p ∨ ~ q ∧ ~ p ∨ ~ ~ q (De Morgans Law) ≡ p ∨ ~ q ∧ ~ p ∨ q Hence Proved.

E M B I B E

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 1 - Mathematical Logic>Exercise 1.4

Maharashtra Board Solutions for Chapter: Mathematical Logic, Exercise 4: Exercise 1.4

Author:Maharashtra Board

Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Chapter: Mathematical Logic, Exercise 4: Exercise 1.4

Attempt the free practice questions on Chapter 1: Mathematical Logic, Exercise 4: Exercise 1.4 with hints and solutions to strengthen your understanding. Mathematics & Statistics (Arts & Science) Part 1 Standard 12 solutions are prepared by Experienced Embibe Experts.