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Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B = ØThen (pick the TRUE statement)
The correct answer is B asLet A={1,2,3B={4,5} C={1,6,7}now A∩B=∅ B∩C=∅B∩C=∅ but A∩C≠∅R is not transitive.
A∩A=AR is not reflexive.
A∩B=B∩AR is symmetricSo, A is false as R is not reflexive or transitiveB is true.C is false because R is not transitive or reflexiveD is false because R is symmetric
The binary relation S = Φ (empty set) on set A = {1, 2,3} is
Explanation:
Thus, option (D) is correct.
Which of the following sets are null sets ?
There are some sets that do not contain any element at all. For example, the set of months with 32 days. We call a set with no elements the null or empty set. It is represented by the symbol { } or Ø.
Number of subsets of a set of order three is
Number of subset = 2norder 3 = 23⇒ 8
"n/m" means that n is a factor of m, then the relation T is
′/′ is reflexive since every natural number is a factor of itself that in n/n for n∈N.′/′ is transitive if n is a factor of m and m is a factor of P, then n is surely a factor of P.However, ′/′ is not symmetric.example, 2 is a factor of 4 but 4 is not a factor of 2.
The number of elements in the Power set P(S) of the set S = [ [ Φ] , 1, [ 2, 3 ]] is
If A and B are sets and A∪ B= A ∩ B, then
Let S be an infinite set and S1, S2, S3, ..., Sn be sets such that S1 ∪S2 ∪S3∪ .......Sn = S then
Let S = S1 ∪ S2 ∪ S3 ∪ .... Sn . For S to be infinite set, atleast one of sets Si must be infinite, if all Si were finite, then S will also be finite.
If X and Y are two sets, then X ∩ (Y ∪ X) C equals
If f : X -> Y and a, b ⊆ X, then f (a ∩ b) is equal to
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