Given the following sets, select the statement below that is true.

A = {l, a, t, e, r}, B = {l, a, t, e}, C = {t, a, l, e}, D = {e, a, t}

B ⊂ C and C ⊆ A
C ⊆ B and D ⊂ B
D ⊂ A and A ⊂ D
B ⊂ A and C ⊂ D
D ⊆ A and A ⊂ C

B ⊂ C and C ⊆ A ---- false AND true ---> false

C ⊆ B and D ⊂ B
D ⊂ A and A ⊂ D ---- true AND false ---> false
B ⊂ A and C ⊂ D
D ⊆ A and A ⊂ C

try the others, remember that for
true/false AND true/false , only true AND true ---> true
any other combination is false.

This one is particularly confusing to me :/

To determine which statement is true, we need to understand the symbols ⊂ and ⊆.

⊂ means "subset". If set A is a subset of set B, it means that every element in A is also in B. In other words, all the elements in A are contained within B, but B may also have additional elements.

⊆ means "subset or equal". If set A is a subset or equal to set B, it means that every element in A is also in B, and B may have additional elements. In this case, A and B can be the same set.

Now let's evaluate the given statements:

Statement 1: B ⊂ C and C ⊆ A
This means that every element in B is also in C, and every element in C is also in A. Looking at the sets:
B = {l, a, t, e}
C = {t, a, l, e}
A = {l, a, t, e, r}
This statement is true since B is a subset of C and C is a subset of A.

Statement 2: C ⊆ B and D ⊂ B
This means that every element in C is also in B, and D is a proper subset of B (meaning D is a subset of B but not equal to B). Looking at the sets:
C = {t, a, l, e}
B = {l, a, t, e}
D = {e, a, t}
This statement is not true because D is not a proper subset of B.

Statement 3: D ⊂ A and A ⊂ D
This means that every element in D is also in A, and A is a proper subset of D. Looking at the sets:
D = {e, a, t}
A = {l, a, t, e, r}
This statement is not true because A is not a proper subset of D.

Statement 4: B ⊂ A and C ⊂ D
This means that every element in B is also in A, and every element in C is also in D. Looking at the sets:
B = {l, a, t, e}
A = {l, a, t, e, r}
C = {t, a, l, e}
D = {e, a, t}
This statement is not true because C is not a subset of D.

Statement 5: D ⊆ A and A ⊂ C
This means that every element in D is also in A, and A is a proper subset of C. Looking at the sets:
D = {e, a, t}
A = {l, a, t, e, r}
C = {t, a, l, e}
This statement is not true because A is not a proper subset of C.

Therefore, the true statement is:
B ⊂ C and C ⊆ A