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3 years ago

Let U represent the set of all people that frequently visit a certain restaurant, surveyed about which food they like best. Let

Mathematics

1 answer:

ankoles [38]3 years ago

7 0

Answer:

a) (C∪P)-B

b) (U-B)∩(U-C)∩(U-P)

c) B∩C∩P

d) P-(B∪C)

e) (B∪C)-P

Step-by-step explanation:

We can use three operations between sets:

Union: X∪Y is the set of elements that belong to X or belong to Y
Intersection: X∩Y is the set of elements that belong to X and belong to Y
Difference: X-Y is the set of elements that belong to X and NOT belong to Y.

The sets we can use in each part are U,B,C and P

a) A customer that likes corn dogs belongs to C, and a customer that likes pizza belongs to P, then a customer who likes corn dogs or pizza belongs to C∪P. The customers from this problem do not like burgers, so they don't belong to B. From this, the required set is (C∪P)-B

b) The customers do not like burgers, so they do not belong to B. However, they visit the restaurant so they belong to U. Thus, the customers belong to U-B. Similarly, because the customers do not like corn dogs and do not like pizza, they belong to U-C and U-P. Then the set of customers is (U-B)∩(U-C)∩(U-P).

c) The customers are in B, C and P so they belong to B∩C∩P.

d) The customers belong to P (they like pizza) but they do not belong to (B∪C), thus they belong to P-(B∪C)

e) The customers belong to B∪C but they do not belong to P, so the required set is (B∪C)-P.

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The pattern here is

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