Answer :
Aftre solving, the all option is false except option c. Only option c, ∅×A=∅ is correct because cartesian product with non empty set with empty set alsways gives empty set.
In the givn question we have to find which statement is true.
To solve the question we let;
A={1,2,3}; B={2,3,4}; C={2,3}
(a) The first option is (A – C) ∩ (A – B) = A – (B ∪ C)
Now solving the both side by putting the value
({1,2,3} – {2,3}) ∩ ({1,2,3} – {2,3,4}) = {1,2,3} – ({2,3,4} ∪ {2,3})
{1} ∩ {1,4} = {1,2,3} – {2,3,4}
{1} = {1,4} (False)
(b) If A ∩ B = ∅, then A ⊂ B
As we know that if If A ∩ B = ∅, then A=∅ and B=∅. That means both A and B will be empty set. So the option B is false.
(c) ∅ X A = ∅
As we know that cartesian product with non empty set with empty set alsways gives empty set. SO the option C is correct.
(d) (A – B) ∪ (B – C) = A – C
Now solving the both side by putting the value
({1,2,3} – {2,3,4}) ∪ ({2,3,4} – {2,3}) = {1,2,3} – {2,3}
{1,4} ∪ {4} = {1}
{1,4} = {1} (False)
(e) ∅ ∩ {∅} = ∅ (False)
(f) B X A = A X B (False)
To learn more about sets link is here
brainly.com/question/18877138
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