Fill in the blanks:
(i) If x is not an element of A, we write ___________
(ii) If number of elements in A is 5, we write ___________
(iii) The members of a set are called its ___________
(iv) If A is a non-empty set, we write, ___________
(v) If A = φ, then n(A) = ___________
(vi) The collection of all persons on earth is a ___________ set.
Answer
(i) If x is not an element of A, we write x ∉ A.
(ii) If number of elements in A is 5, we write n(A) = 5.
(iii) The members of a set are called its elements (or members or points).
(iv) If A is a non-empty set, we write, A ≠ φ.
(v) If A = φ, then n(A) = 0.
(vi) The collection of all persons on earth is a finite set.
Write (T) for true and (F) for false for each of the following statements:
(i) If A = set of prime numbers, then 9 ∈ A. ___________
(ii) If A = set of even integers, then -8 ∈ A. ___________
(iii) If M = N, then n(M) = n(N). ___________
(iv) If n(A) = n(B), then A = B. ___________
(v) {1, 1, 2, 3} = {1, 2, 3}. ___________
(vi) Collection of tasty fruits is a set. ___________
Answer
(i) 9 = 3 × 3 is a composite number, not a prime number. So, 9 ∉ A.
(F)
(ii) -8 is an even integer, so it is a member of the set of even integers.
(T)
(iii) If M = N, both sets have exactly the same elements, so they have the same cardinal number.
(T)
(iv) Two sets with the same cardinal number are equivalent, but need not be equal.
(F)
(v) The repetition of elements in a set is meaningless, so {1, 1, 2, 3} = {1, 2, 3}.
(T)
(vi) The word 'tasty' is subjective, so the collection is not well defined and hence not a set.
(F)