SOLUTION: Given the following sets, select the statement below that is NOT true. A = {r, i, s, k, e, d}, B = {r, i, s, e}, C = {s, i, r} B ⊂ A or A ⊂ C or B ⊆ A or C &#

Let's go through them:

B ⊂ A

Substitute the actual sets for the capital letters that represent them.

{r, i, s, e} ⊂ {r, i, s, k, e, d}

That is true because all four elements listed on the left of this
symbol ⊂ are all on the right of that symbol, and B doesn't contain
all of A, so it's true that B is a proper subset of A.  

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A ⊂ C

Substitute the actual sets for the capital letters that represent them.

{r, i, s, k, e, d}  ⊂ {s, i, r}

That is very false because the elements listed on the left of this
symbol ⊂ are certainly not all on the right of that symbol, and B doesn't
contain all of A, so it's false that B is a proper subset of A. 

So that one is false

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B ⊆ A

That means "B ⊂ A or B = A" and we've already shown that B ⊂ A is true above.

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C ⊆ A

Substitute the actual sets for the capital letters that represent them.

{s, i, r} ⊆ {r, i, s, k, e, d}

That is true because all three elements listed on the left of this
symbol ⊆ are all on the right of that symbol. The only difference
between the symbols ⊆ and ⊂ is that the first one allows the set on
the left to actually be equal to the set on the right. This symbol ⊂ 
does not.  It requires that the set on the left have fewer elements 
than the one on the right.

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C ⊆ B

Substitute the actual sets for the capital letters that represent them

{s, i, r} ⊆ {r, i, s, e}

That is true because all three elements listed on the left of this
symbol ⊆ are all on the right of that symbol.

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So A ⊂ C is the only one that's false.

Edwin