Advertisements
Advertisements
Question
State, if the following pair of a set is equal or not:
A = {x : x ∈ N, x < 3} and B = {y : y2 - 3y + 2 = 0}
Solution
A = {x : x ∈ N, x < 3}
= {1, 2}
B = {y : y2 - 3y + 2 = 0}
y2 - 3y + 2 = 0
⇒ y2 - 2y - y + 2 = 0
⇒ y(y - 2) -1(y - 2) = 0
⇒ (y - 2)(y - 1) = 0
∴ Either y - 2 = 0
⇒ y = 2
Or
y - 1 = 0
⇒ y = 1
∴ B = {1, 2}
Now we see that elements of sets A and B are the same (identical).
∴ Sets A and B are equal.
APPEARS IN
RELATED QUESTIONS
Write with reason, Whether the following set is finite or infinite.
A = {x | x < 10, x is a natural number}
Write with reason, whether the following set is finite or infinite.
Set of apparatus in the laboratory
State the following sets are finite or infinite:
P = {y : y = 3x -2, x ∈ N & x > 5}
State, if the following pair of a set is equivalent or not:
A = {x : x ∈ N and 11 ≥ 2x – 1} and B = {y : y ∈ W and 3 ≤ y ≤ 9}
State, if the following pair of a set is equivalent or not:
Set of integers and set of natural numbers.
State, if the following pair of a set is equal or not :
A = {2, 4, 6, 8} and B = {2n : n ∈ N and n < 5}
Identify the following sets are equivalent or unequal or equal sets?
C = {2, 3, 4, 5}
D = {x : x ∈ W, 1 < x < 5}
Find the number of subsets and the number of proper subsets of the following set
W = {red, blue, yellow}
If n[P(A)] = 256, find n(A)
If A = {x, y, z} then the number of non-empty subsets of A is
