Find the cardinal number of the following set. B = { x : x ∈ N and 2 < x < 7 }

Given, B = { x : x ∈ N and 2 < x < 7 } As given, the natural numbers less than 7 and greater than 2 are 3 , 4 , 5 , 6 . The number of distinct elements in a set is called the cardinal number of the set. The cardinal number of a set A is denoted by n A . Hence, B = { x : x ∈ N and 2 < x < 7 } ⇒ n B = 4 . Therefore, the cardinal number of the set is n B = 4 .

Find the cardinal number of the following set. B = { x : x ∈ N and 2 < x < 7 }

Given, B = { x : x ∈ N and 2 < x < 7 } As given, the natural numbers less than 7 and greater than 2 are 3 , 4 , 5 , 6 . The number of distinct elements in a set is called the cardinal number of the set. The cardinal number of a set A is denoted by n A . Hence, B = { x : x ∈ N and 2 < x < 7 } ⇒ n B = 4 . Therefore, the cardinal number of the set is n B = 4 .

Find the cardinal number of the following set. C = { x : x ∈ W and 3 x - 2 ≤ 7 }

Given, C = { x : x ∈ W and 3 x - 2 ≤ 7 } We know that the whole numbers are 0 , 1 , 2 , 3 , . . . . . Putting the values of x in the inequation 3 x - 2 ≤ 7 , we get, When x = 0 , 3 x - 2 = 3 × 0 - 2 = - 2 ≤ 7 When x = 1 , 3 x - 2 = 3 × 1 - 2 = 1 ≤ 7 When x = 2 , 3 x - 2 = 3 × 2 - 2 = 4 ≤ 7 When x = 3 , 3 x - 2 = 3 × 3 - 2 = 7 ≤ 7 When x = 4 , 3 x - 2 = 3 × 4 - 2 = 10 > 7 ∴ C = 0 , 1 , 2 , 3 The number of distinct elements in a set is called the cardinal number of the set. The cardinal number of a set A is denoted by n A . Hence, C = { x : x ∈ W and 3 x - 2 ≤ 7 } ⇒ C = { 0 , 1 , 2 , 3 } . Therefore, the cardinal number of the set is n C = 4 .

Find the cardinal number of the following set. D = { x : x ∈ N and x ≤ 5 }

Given, D = { x : x ∈ N and x ≤ 5 } The natural numbers are 1 , 2 , 3 , 4 , . . . . . . So, the natural numbers x ≤ 5 are 1 , 2 , 3 , 4 , 5 . The number of distinct elements in a set is called the cardinal number of the set. The cardinal number of a set A is denoted by n A . Hence, D = { x : x ∈ N and x ≤ 5 } ⇒ D = { 1 , 2 , 3 , 4 , 5 } . Therefore, the cardinal number of the set is n D = 5 .

Find the cardinal number of the following set. E = { x : x ∈ Z and 3 < x < 4 }

Given, E = { x : x ∈ Z and 3 < x < 4 } We know that the integers are . . . . . . - 4 , - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 , . . . . . . . The number of integers 3 < x < 4 = 0 ∴ E = ϕ The number of distinct elements in a set is called the cardinal number of the set. The cardinal number of a set A is denoted by n A . Hence, E = { x : x ∈ Z and 3 < x < 4 } ⇒ E = ϕ . Therefore, the cardinal number of the set is n ϕ = 0 .