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Let R be a nonempty relation on a collection of sets defined by ARB if and only if A ∩ B = Ø
Then (pick the TRUE statement)
The correct answer is B asLet A={1,2,3
B={4,5}
C={1,6,7}
now
A∩B=∅
B∩C=∅
B∩C=∅ but
A∩C≠∅
R is not transitive.
A∩A=A
R is not reflexive.
A∩B=B∩A
R is symmetric
So,
A is false as
R is not reflexive or transitive
B is true.
C is false because
R is not transitive or reflexive
D is false because
R is symmetric
Explanation:
Thus, option (D) is correct.
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 subset = 2^{n}
order 3 = 2^{3}
⇒ 8
′/′ 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
Let S be an infinite set and S_{1}, S_{2}, S_{3}, ..., S_{n} be sets such that S_{1} ∪S_{2} ∪S_{3}∪ .......S_{n} = S then
Let S = S1 ∪ S2 ∪ S3 ∪ .... Sn .
For S to be infinite set, atleast one of sets S_{i} must be infinite,
if all S_{i} were finite, then S will also be finite.
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