## Let A = {n ℤ | n = 5r for some integer r} and B = {m ℤ | m = 20s for some integer s}. Determine which of the following statements are true a

Question

Let A = {n ℤ | n = 5r for some integer r} and B = {m ℤ | m = 20s for some integer s}. Determine which of the following statements are true and which are false. (Enter TRUE if the statement is true, and enter a number that could be used as the basis for a counterexample if the statement is false).

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2 weeks 2021-09-10T09:07:50+00:00 1 Answer 0

Incomplete question

This is the complete aspect of the question

a. Is this true or false

A⊆B?

b. Is this true or false

B⊆A?

Step-by-step explanation:

Given that

A = {n ℤ | n = 5r for some integer r}

Integer are positive and negative whole numbers

A={…-20,-15,-10,-5,0,5,10,15,20…}

Also,

B ={mℤ |m = 20s for some integer s}.

Then,

B={….-80,-40,-20,0,20,40,80….}

a. In mathematics, a set A is contained in B if every element in A is found in B

Then,

A⊆B

Then looking at A and B, not all element in A can be found in B e.g, 10, 15,25,-10,-25 and so, the law doesn’t hold

Then, A⊆B is false

b. B⊆A, now every element in B can be found in A, then this is true and then B is contain in A