Write each of the following intervals in the set-builder from:

(i) A = (–2, 3)

(ii) B = [4, 10]

(iii) C = [–1, 8)

(iv) D = (4, 9]

(v) E = [–10, 0)

(vi) F = (0, 5]

Write each of the following intervals in the set-builder from:

(i) A = (–2, 3)

(ii) B = [4, 10]

(iii) C = [–1, 8)

(iv) D = (4, 9]

(v) E = [–10, 0)

(vi) F = (0, 5]

If A = {5} and B = {5, 6}, write down all possible subsets of A × B.

Mark the correct alternative in the following:

If R is a relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B is

Mark the correct alternative in the following:

Let R be a relation from a set A to a set B, then

If A = {1} and B = {{1}, 2} then show that A ⊄ B.

Hint 1 ϵ A but 1⊄ B.

Prove that A ⊆B, B⊆ C and C⊆ A ⇒A = C.

Write down all subsets of each of the following sets:

(i) A = {A}

(ii) B = {a, b}

(iii) C = {–2, 3}

(iv) D = {–1, 0, 1}

(v) E =ϕ

(vi) F = {2, {3}}

(vii) G = {3, 4, {5, 6}}

State in each case whether A ⊂ B or A ⊄ B.

A = {x : x is an integer}, B = {x: x is a rational number}

Let A = {{1,2,3}, {4,5}, {6,7,8}}. Determine which of the following is true or false:

(i) 1 A

(ii) {1,2,3} ⊂ A

(iii) {6,7,8} A

(iv) {2, ϕ} ⊂ A

(v) 2 ⊂ A

(vi) {2,{1}} A

(vii) {{2}}, {1}} A

(viii) {ϕ,{ϕ}, {1, ϕ}} ⊂ A.