Question

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}

Answer 1

`M \cap F = \{c, d\}`.

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` "cap" symbol. (As a side note, the symbol for the union of two sets is
`\cup` "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
`M` and
`F` will be written as
`M \cap F`.

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
`M` as an example.

• The first element of set
  `M` is
  `a`. Is element
  `a` in set
  `F`? This element is only found in set
  `M` but not in set
  `F`. Do not add it to the intersection.
• The second element of set
  `M` is
  `b`. Is element
  `b` in set
  `F`? This element is only found in set
  `M` but not in set
  `F`. Do not add it to the intersection.
• The third element of set
  `M` is
  `c`. Is element
  `c` in set
  `F`? This element is found in both set
  `M` and set
  `F`. Add it to the intersection
  `M \cap F`.
• The fourth element of set
  `M` is
  `d`. Is element
  `d` in set
  `F`? This element is found in both set
  `M` and set
  `F`. Add it to the intersection
  `M \cap F`.

`M \cap F` will eventually contain two elements:
`c` and
`d`. In symbols:
`M \cap F = \{c, d\}`.