Advertisements
Advertisements
Question
Decide which of the following are equal sets and which are not. Justify your answer.
- A = {x | 3x - 1 = 2}
- B = {x | x is a natural number but x is neither prime nor composite}
- C = {x | x ∈ N, x < 2}
Solution
i. Since, A = {x | 3x - 1 = 2} ...(Rule method)
3x - 1 = 2
3x = 3
∴ x = 1
x = {1} ...(Roster Method)
ii. B = {x | x is a natural number but x is neither prime nor composite} ...(Rule method)
B = {1} ...(Listing method)
iii. C = {x | x ∈ N, x < 2} ...(Rule method)
N = {1, 2, 3, 4, .....}
C = {1} ...(Listing method)
From (i), (ii) and (iii)
So, A = B = C
APPEARS IN
RELATED QUESTIONS
In the following, state whether A = B or not:
A = {a, b, c, d}; B = {d, c, b, a}
In the following, state whether A = B or not:
A = {2, 4, 6, 8, 10}; B = {x : x is positive even integer and x ≤ 10}
In the following, state whether A = B or not:
A = {x : x is a multiple of 10}; B = {10, 15, 20, 25, 30, ...}
Which of the following sets are equal?
(i) \[A = \left\{ 1, 2, 3 \right\};\]
(ii) \[B = \left\{ x \in R : x^2 - 2x + 1 = 0 \right\};\]
(iii) \[C = \left\{ 1, 2, 2, 3 \right\};\]
(iv) \[D = \left\{ x \in R : x^3 - 6 x^2 + 11x - 6 = 0 \right\}\]
Are the following sets equal?
A = {x : x is a letter in the word reap}:
B = {x : x is a letter in the word paper};
C = {x : x is a letter in the word rope}.
From the sets given below, pair the equivalent sets:
\[A = \left\{ 1, 2, 3 \right\}, B = \left\{ t, p, q, r, s \right\}, C = \left\{ \alpha, \beta, \gamma \right\}, D = \left\{ a, e, i, o, u \right\} .\]
Are the following pairs of sets equal? Give reasons.
A = {2, 3}, B = {x : x is a solution of x2 + 5x + 6 = 0}
Show that the set of letters needed to spell "CATARACT" and the set of letters needed to spell "TRACT" are equal.
The set \[\left( A \cup B' \right)' \cup \left( B \cap C \right)\] is equal to
Decide whether sets A and B are equal sets. Give reason for your answer.
A = Even prime numbers
