Question

A = {x / x is an odd number between 5 and 21} is same as------------
a. A = {5,7,9,11,13,15,17,19}
b. A = {5,7,9,11,13,15,17,19,21}
c. A = {x : x is an odd number between 5 and 21}
d. A = {7,9,11,13,15,17,19,21}

Answer 1

Answer on Question #51201 - Math - Set Theory

A = {x / x is an odd number between 5 and 21} is same as---

a. $A_{a} = \{5,7,9,11,13,15,17,19\}$

b. $A_{b} = \{5,7,9,11,13,15,17,19,21\}$

c. $A_{c} = \{x:x$ is an odd number between 5 and 21}

d. $A_{d} = \{7,9,11,13,15,17,19,21\}$

Solution

By the definition of origin set we have that if $x \in A$ then $x$ is odd and $5 < x < 21$ .

Let's check each of the given variants:

a. $A_{a} = \{5,7,9,11,13,15,17,19\}$ , since $5 \in A_{a}$ and $5 \neq 5$ then $A_{a} \neq A$

b. $A_{b} = \{5,7,9,11,13,15,17,19,21\}$ , since $5 \in A_{b}$ and $5 \neq 5$ then $A_{b} \neq A$

d. $A_{d} = \{7,9,11,13,15,17,19,21\}$ , since $21 \in A_{d}$ and $21 \neq 21$ then $A_{d} \neq A$

c. $A_{c} = \{x : x$ is an odd number between 5 and 21}, so if $x \in A_{c}$ then $x$ is odd and $5 < x < 21$ .

Thus, if $x \in A_c$ then $x \in A$ , and vice versa: if $x \in A$ , then $x \in A_c$ . This means that $A_c = A$

Answer: c.

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