Show that the set of letters needed to spell “CATARACT” and the set of letters needed to spell “TRACT” are equal.

From the sets given below, select equal sets and equivalent sets.

A={0, a}, B= {1, 2, 3, 4} C= {4, 8, 12},

D = {3, 1, 2, 4}, E={1, 0}, F = {8, 4, 12}

G={1, 5, 7, 11}, H={a, b}

Which of the following sets are equal?

A= {x:x ∈ N, x < 3},

B= {1, 2}, C= {3, 1}

D = {x : x ∈ N, x is odd, x < 5},

E= (1, 2, 1, 1}, F= {1, 1, 3}.

Which of the following statements are true? Give a reason to support your answer.

(i) For any two sets A and B either A B or B A.

(ii) Every subset of an infinite set is infinite.

(iii) Every subset of a finite set is finite.

(iv) Every set has a proper subset.

(v) {a,b,a,b,a,b,….} is an infinite set.

(vi) {a,b,c} and {1,2,3} are equivalent sets.

(vii) A set can have infinitely many subsets.

State whether the following statements are true or false:

(i) 1 { 1,2,3}

(ii) a ⊂ {b,c,a}

(iii) {a} {a,b,c}

(iv) {a,b} = {a,a,b,b,a}

(v) The set {x:x + 8 = 8} is the null set.