Short Answer TypeLet U = {1, 2, 3, 4, 5,......}, write the complement of the following sets :
(a) {x : x is an odd number}
(b) {x : x is an even number}
(c) {1, 4, 6, 8, 10, 12, 14, 15, 16,......}
Write whether the given statements are true or false :
(i) Every set has a proper subset
(ii) If A is a subset of B and B is a subset of C, then A is not a subset of C.
Which of the following are sets ? Justify your answer. Also, write the elements if the collection
is a set.
(a) Collection of all prime numbers less than 30.
(b) Collection of all divisors of 24.
(c) Collection of all prime divisors of 180.
(d) Collection of renowned mathematicians of the world.
(e) Collection of rainbow colours.
(f) Collection of fat people in your town.
(g) Collection of roots of quadratic equation x2-7x+ 12 = 0 (h) Collection of months of the year which have 31 days.
Multiple Choice QuestionsLet A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A x B, each having at least three elements is:
219
256
275
275
A.
219
Given,
n(A) = 4 n (B) =2
⇒ n(A x B) = 8
Total number of subsets of set (A x B)= 28
Number of subsets of set A x B having no element (i.e, Φ) = 1
Number of subsets of set AxB having two elements = 8C1
Number of subsets of set A x B having two elements = 8C2
therefore, the number of subsets having atleast three elements,
= 28 x (1+8C1 + 8C2)
= 28 -1-8-28
= 28 -37
= 256-37 = 219
Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is
256
220
219
219
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