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Let x be a non empty set and p (x) be the set of all subsets of x. For A, B belong to the p(x), power set of x, ARB iff A intersection B =empty set then relation is A) reflexive B) symmetric C) transitive D) equivalence Please answer quickly

Let x be a non empty set and p (x) be the set of all subsets of x. For A, B belong to the p(x), power set of x, ARB iff A intersection B =empty set then relation is 
A) reflexive
B) symmetric 
C) transitive 
D) equivalence 
Please answer quickly 

Grade:12

2 Answers

mental mind
10 Points
5 years ago
Without loss of generality consider a set X and a power set p(X). By equivalence relation means it consists 3 property
(1)symmetric
(2)reflexive
(3)transitivity
To discard option (a) let A be a non empty set then A∩A≠⍉ 
 
To discard option (b) Take A={1,2} B={3,4} and C={2,5} then (A∩B)∩C=⍉ but A∩C≠⍉ (verify).
 
only (C) is true take any two adjoint matrix.
 
Note : All sets belongs to the power set.
mental mind
10 Points
5 years ago
ooops sorry there is a mistake Only B is true i did not get attentionn on options. symmetric is mention in B option. 
 
 

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