Given A={1,3,6,8,9,12,15} and B={6,9,12},which of the following statements is true?BUA A∩B=∅. Aand B are disjont sets Bi s the compliment of A

We have:

A={1,3,6,8,9,12,15}

B={6,9,12}

Let's analyze the statements:

1) B is the complement of A:

The complement of a set W is the set with all the elements in the universal set that do not belong to the set W, in this case, you can see that the 3 elements of set B do also belong to set A, then this statement is false.

2) A and B are disjoint sets:

Two sets are disjoint if they do not share any element, in this case, the 3 elements of B also belong to A, then the sets share elements, which means that the sets are not disjoint, so this statement is false.

3) A∩B=∅

A∩B is the set of all the common elements of A and B, in this case we have:

A∩B = {6, 9, 12}

Then the statement is false.

4) BUA = A

BUA is the union of set A and B, and it's defined as the combination of all elements of A and B (such that there are no repeated elements)

Or we can write this as:

A + B - A∩B  = {6,9,12} + {1,3,6,8,9,12,15} - {6,9,12}

                     = {1,3,6,8,9,12,15} = A

Then BUA = A

This is true.

both equations and proportions are better.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°