Sure, let's prove that (A ∪ B) - B = A - B for any sets A and B.

Step 1: Let's take an element x in (A ∪ B) - B. This means that x is in A or x is in B (because of the union), and x is not in B (because of the subtraction). So, the only possibility left is that x is in A and not in B.

Step 2: Now, let's take an element x in A - B. This means that x is in A and x is not in B.

Step 3: From steps 1 and 2, we can see that an element x is in (A ∪ B) - B if and only if x is in A - B. Therefore, (A ∪ B) - B = A - B.

So, we have proved that (A ∪ B) - B = A - B for any sets A and B.

Question

Sure, let's prove that (A ∪ B) - B = A - B for any sets A and B.

Step 1: Let's take an element x in (A ∪ B) - B. This means that x is in A or x is in B (because of the union), and x is not in B (because of the subtraction). So, the only possibility left is that x is in A and not in B.

Step 2: Now, let's take an element x in A - B. This means that x is in A and x is not in B.

Step 3: From steps 1 and 2, we can see that an element x is in (A ∪ B) - B if and only if x is in A - B. Therefore, (A ∪ B) - B = A - B.

So, we have proved that (A ∪ B) - B = A - B for any sets A and B.

Knowee AI · Accepted Answer

Sure, let's prove that (A ∪ B) - B = A - B for any sets A and B.

Step 1: Let's take an element x in (A ∪ B) - B. This means that x is in A or x is in B (because of the union), and x is not in B (because of the subtraction). So, the only possibility left is that x is in A and not in B.

Step 2: Now, let's take an element x in A - B. This means that x is in A and x is not in B.

Step 3: From steps 1 and 2, we can see that an element x is in (A ∪ B) - B if and only if x is in A - B. Therefore, (A ∪ B) - B = A - B.

So, we have proved that (A ∪ B) - B = A - B for any sets A and B.

Prove or disprove that (A ∪ B) − B = A − B for any sets A and B.

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