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

B = x ∈ U

C = x likes Corn Dogs

P = x ∈ U

(Assume these sets are not disjoint.) Write the statement that refers to: B c ∪ C c ∪ P c.

a) The set of customers who do not like any Burger but do like Corn Dogs or Pizza.

b) The set of customers who do not like Burgers, Corn Dogs, and Pizza.

c) The set of customers who like all three foods given.

d) The set of customers who do not like Burgers or Corn Dogs but do Pizza.

e) The set of customers who do not like Pizza but Corn Dogs or Burgers.

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.