State whether the following sets are finite or infinite. (i) A = {x : – InterviewSolution

InterviewSolution

1.

State whether the following sets are finite or infinite. (i) A = {x : x is a multiple of 5, x ∈ N}. (ii) B = {0, 1, 2, 3, 4, 75}. (iii) The set of all positive integers greater than 50.

Answer»

(i) A = {5, 10, 15, 20, …… }

∴ A is an infinite set

(ii) Finite

(iii) Let X be the set of all positive integers greater than 50

Then X = {51, 52, 53, ….. }

∴ X is an infinite set.

Discussion

No Comment Found

Related InterviewSolutions

If A = {2, 3, 5, 7,11} and B = {5, 7, 9, 11, 13}, find A ∆ B.
(i) If n(A) = 25, n(B) = 40, n(A ∪ B) = 50 and n(B’) = 25, find n(A ∩ B) and n(U).(ii) If n(A) = 300, n(A ∪ B) = 500, n(A ∩ B) = 50 and n(B’) = 350, find n(B) and n(U).
If U = {x : x ∈ N and x < 10}, A = {1, 2, 3, 5, 8} and B = {2, 5, 6, 7, 9}, then n[(A ∪ B)’] is (1) 1 (2) 2 (3) 4 (4) 8
Which of the following is true? (1) A – B = A ∩ B (2) A – B = B – A (3) (A ∪ B)’ = A’ ∪ B’ (4) (A ∩ B)’ = A’ ∪ B’
If A ∪ B = A ∩ B, then (1) A ≠ B (2) A = B (3) A ⊂ B (4) B ⊂ A
In a class of 50 boys, 35 boys play carom and 20 boys play chess then the number of boys play both games is (1) 5 (2) 30 (3) 15(4) 10
From the adjacent diagram n[P(A ∆ B)] is (1) 8 (2) 16 (3) 32 (4) 64
If n(A) = 10 and n(B) = 15 then the minimum and maximum number of elements in A ∩ B is (1) (10, 15) (2) (15, 10) (3) (10, 0) (4) (0, 10)
For any three sets P, Q and R, P – (Q ∩ R) is (1) P – (Q ∪ R) (2) (P ∩ Q) – R (3) (P – Q) ∪ (P – R) (4) (P – Q) ∩ (P – R)
Verify n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C) for the following sets. (i) A = {a, c, e, f, h}, B = {c, d, e, f} and C = {a, b, c, f} (ii) A = {1, 3, 5}, B = {2, 3, 5, 6} and C = {1, 5, 6, 7}.