Question

Consider the following sets and fill up the blank in the statement given below with = or ≠ 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

Answer 1

We know that two sets A and B are equal if every element in A belongs to B and every element in B belongs to A.

(i) First three natural numbers are 1, 2, 3 so,B = {1,2,3} and A = {1,2,3}
∴ A = B
(ii) A = {1,2,3}
and E = {a, e , i, o, u}
∴ A ≠ E
(iii) C = {a, b, c, d}
D = {d, c, a, b}
∴ C = D
(iv) D = {d, c, a, b}
F = set of vowels = {a, e, i, o, u}
∴ D ≠ F
(v) F = set of vowels = {a, e, i, o, u}
A = {1, 2, 3}
∴ F ≠ A
(vi) D = {d, c, a, b}
E = (a, e, i, o, u}
∴ D ≠ E
(vii) F = set of vowels = {a, e, i, o, u}
B = first three natural numbers = {1, 2, 3}
∴ F ≠ B

Answer 2

Dear Student,

Solution:

Before answering the question,we must write the sets B and F in roster form.

Set B = { The first three natural numbers}

As we know that natural numbers are 1,2,3,4,5,...

So,first three numbers are 1,2,3

B ={1,2,3}

Set F = {set of vowels in English Alphabet}

F = {a, e, i, o, u};

(i) A = B; Since both are equal

(ii) A ≠ E ; since both are not equal

(iii) C = D; since both sets are equal because order does not matter

(iv) D ≠ F; since both are not equal

(v) F ≠ A; Since both sets have different element

(vi) D ≠ E; since both set have different elements

(vii) F ≠ B ;since both set are not equal

Hope it helps you.