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Definition of Sets

Which of the ...

Question

Which of the following sets are equivalent?
(i) $A = {2, 4, 6, 8, 10}, B = {1, 3, 5, 7, 9}$
(ii) $X = {x : x \in N, 1 < x < 6}, Y =$ { $x : x$ is a vowel in the English Alphabet }
(iii) $P =$ ${$ $x : x$ is a prime number and $5 < x < 23$ $}$
$Q = {x : x \in W, 1 < x < 5}$

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Solution

Given sets in $1, 2, 3$ are not equivalent sets. since the elements in both sets are not equal.

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Similar questions

Q. Find the cardinal number of the following sets
(i)

A =

{

x : x = 5^{n}, n \in N

n < 5

}

B =

{

x : x

is a consonant in English Alphabet

}

X =

{

x : x

is an prime number

}

P = {x : x < 0, x \in W}

Q = {x : - 3 \leq x \leq 5, x \in Z}

Q. State which of the following sets are disjoint
(i)

A = {2, 4, 6, 8}; B =

{

x : x

is an even number

< 10, x \in N}

X = {1, 3, 5, 7, 9}, Y = {0, 2, 4, 6, 8, 10}

P =

{

x : x

< 15

}

Q =

{

x : x

is a multiple of 2 and

x < 16

}

R = {a, b, c, d, e}, S = {d, e, a, b, c}

Q. Write the following sets in Roster form
(i)

A = {x : x \in N, 2 < X \leq 10}

B = {x : x \in Z, - \frac{1}{2} < X < \frac{11}{2}}

C =

x : x

is a prime number and a divisor of 6 }
(iv)

X =

x : x = 2^{n}, n \in N

n \leq 5

M = {x : x = 2 y - 1, y \leq 5, y \in W}

P =

x : x

x^{2} \leq 16

Q. Taking the set of natural numbers as the universal set, write down the complements of the following set:

(i) {x : x

is an even natural number

}

(i i) {x : x

is an odd narutal number

}

(i i i) {x : x

is a positive multiple of

3}

(i v) {x : x is a prime number}

(v) {x : x is a natural number divisible by 3 and 5}

(v i) {x : x is a perfect square}

(v i i) {x : x is a perfect cube}

(v i i i) {x : x + 5 = 8}

(i x) {x : 2 x + 5 = 9}

(x) {x : x \geq 7}

(x i) {x : x \in N and 2 x + 1 > 10}

A \cup B

A \cap B

for the following sets.
(i)

A = {0, 1, 2, 4, 6}

B = {- 3, - 1, 0, 2, 4, 5}

A = {2, 4, 6, 8}

B = \emptyset

A = {x : x \in N, x \leq 5}

B =

x : x

is a prime number less than 11}
(iv)

A = {x : x \in N, 2 < x \leq 7}

B = {x : x \in W, 0 \leq x \leq 6}

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