Write the negations of the following. 2 is a rational number.

Given statement is " 2 is a rational number." Let p : 2 is a rational number. The negation of a statement is the opposite truth of given statement and denoted by symbol ~ . Here, negation is ~ p Therefore, the negation of the given statement is “ 2 is not a rational number.”

Write the negations of the following. ∀ n ∈ N , n 2 + n + 2 is divisible by 44 .

Given statement is " ∀ n ∈ N , n 2 + n + 2 is divisible by 44 ." Let p : ∀ n ∈ N , n 2 + n + 2 is divisible by 44 . The negation of "for every" is "there exists" and it can be represented in symbolic form as : ∀ symbol used for "for all" and ∃ symbol used for "there exists". Therefore, the negation of the given statement is" ∃ n ∈ N , n 2 + n + 2 is not divisible by 44 .”

Write the negations of the following. ∃ x ∈ N such that x − 17 < 20 .

Given statement is " ∃ x ∈ N such that x − 17 < 20 ." Let p : ∃ x ∈ N such that x − 17 < 20 . The negation of "for every" is "there exists" and it can be represented in symbolic form as : ∀ symbol used for "for all" and ∃ symbol used for "there exists". Therefore, the negation of the given statement is" ∀ x ∈ N such that x - 17 ≥ 20 .”

E M B I B E

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 1 - Mathematical Logic>Exercise 1.3

Maharashtra Board Solutions for Chapter: Mathematical Logic, Exercise 3: Exercise 1.3

Author:Maharashtra Board

Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Chapter: Mathematical Logic, Exercise 3: Exercise 1.3

Attempt the practice questions on Chapter 1: Mathematical Logic, Exercise 3: Exercise 1.3 with hints and solutions to strengthen your understanding. Mathematics & Statistics (Arts & Science) Part 1 Standard 12 solutions are prepared by Experienced Embibe Experts.