Question

A={a,b,c,1,2,3,octopus,∅,0} B=N C={0} For each of the following statements, select either True or False. a) A∩B={0,1,2,3} Answer 1 b) C−A=∅ Answer 2 c) B∪P(C)=B Answer 3 d) C∈P(C) Answer 4

Answer 1

Answer:a)False b)True c)False d)True

Step-by-step explanation:

Let's consider first that for us the set of the natural numbers is the set of the positive integers and the set of the non-negative numbers is know as the whole number or with notation $N_0$. Then for

a) the N={1,2,3,...} and therefore the common members with A are only {1,2,3} making the statement false, only if stated to consider the set N as all the non-negative numbers the answer would be true, but otherwise it is standarized to understand N as the positive integers and $N_0$ as the non-negative integers.

b)The difference of sets is taking the elements in the first that do not belong to the second, then it would be to withdraw the only element C has, since 0 belongs to A, and therefore C would turn to be an empty set.

c)The set powers of a given set S, denoted P(S), is a set with sets as elements, every subset of S is an element of P(S). Then P(S) is always non-empty, since at least S belongs to P(S). Here $P(C)=\{C, \emptyset \}$, then $P(C)\cup B=\{C, \emptyset ,1,2,3,\ldots \}\ne B$, therefore the statement is false.

d)As explained in c) $P(C)=\{C, \emptyset \},$ then clearly C is an element of P(C), thus the affirmation is true.