Example-12. Consider the sets ∅ , A = {1, 3}, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}. Insert the symbol ⊂ or ⊄ between each of the following pair of sets.

(i) ∅ ….. B     (ii) A ….. B     (iii) A ….. C     (iv) B ….. C

Solution

(i) ∅ ⊂ B, as ∅ is a subset of every set.

(ii) A Ë B, as 3 ∈ A but 3 ∉ B.

(iii) A ⊄ C as 1, 3 ∈ A also belong to C.

(iv) B ⊂ C as every element of B is also an element of C.

EXERCISE - 2.3

1. Which of the following sets are equal?

A = {x : x is a letter in the word FOLLOW}, B = {x : x is a letter in the word FLOW} and C = {x : x is a letter in the word WOLF}

2. Consider the following sets and fill up the blanks with = or ¹ so as to make the statement true.

A = {1, 2, 3};          B = {The first three natural numbers}

C = {a, b, c, d};          D = {d, c, a, b}


E = {a, e, i, o, u};          F = {set of vowels in English Alphabet}

(i) A .... B     (ii) A .... E      (iii) C .... D     (iv) D .... F      (v) F .... A      (vi) D .... E     (vii) F .... B

3. In each of the following, state whether A = B or not.

(i) A = {a, b, c, d}         B = {d, c, a, b}

(ii) A = {4, 8, 12, 16}         B = {8, 4, 16, 18}



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