Sets m and f are defined as follows.
m={a, b,c, d}
f={c, d,e, f}
find the intersection of m and f.
m∩f={c, d}
m∪f={c, d}
m∩f={a, b,c, d,e, f}
m∪f={a, b,c, d,e, f}

.

Step-by-step explanation:

When the question asks for the intersection of the two sets, M, and F, it is asking for the set of all items that are both in set M and in set F. The intersection of two sets is denoted with the "cap" symbol. (As a side note, the symbol for the union of two sets is "cup." The size of the intersection of two sets is always smaller than or equal to the size of their union. Which one holds more stuff? The cap or the cup?) The intersection of set and will be written as .

In practice, start by looking at either of the two sets. It is suggested that you choose the set with the smallest number of elements to begin with.

For each element of the set that you choose, check if that element is also part of the other set. If it is, write it down as a member of the other set.

Taking set as an example.

will eventually contain two elements: and . In symbols: .

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.