please help me fast One of the following sentences is FALSE.Select one:O a.ASAUBO b.ニニASB= ASBC.ANBSBd. Non of themе.= =ASB- 9(A)< P(B)Let A and B be sets such that A = 17 and B= 8. The largest possible value of AUB is:Select one:a. Can not be calculatedb. 25C. 8d. 17e. Non of them

(1) Let A and B be two sets and let A¯=nA To determine the false statements. (a) nA≤nA∪B For any…

Answered: One of the following sentences is…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.1: Sets And Geometry

Problem 12E: For the sets given in Exercise 9, is there a distributive relationship for intersection with respect...

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please help me fast

One of the following sentences is FALSE.
Select one:
O a.
ASAUB
O b.
ニニ
ASB= ASB
C.
ANBSB
d. Non of them
е.
= =
ASB- 9(A)< P(B)
Let A and B be sets such that A = 17 and B= 8. The largest possible value of AUB is:
Select one:
a. Can not be calculated
b. 25
C. 8
d. 17
e. Non of them

Expert Solution

Step 1

(1)

Let A and B be two sets and let $\bar{A} = n (A)$

To determine the false statements.

(a) $n (A) \leq n (A \cup B)$

For any sets A and B, $A \subseteq A \cup B$ .

Then, clearly, $n (A) \leq n (A \cup B)$

Therefore, the statement (a) is true.

(b) $n (A) \leq n (B) \Rightarrow A \subseteq B$

Consider two sets, $A = \{1, 2\} and B = \{3, 4, 5\}$ .

Here, $n (A) \leq n (B)$ but A is not a subset of B.

Therefore, $n (A) \leq n (B) \Rightarrow A \subseteq B$ is not true.

Hence, the statement (b) is false.

Step 2

By definition, $A \cap B \subseteq B$ .

Therefore, $n (A \cap B) \leq n (B)$ .

Hence, the statement (c) is true.

(d) Since (b) is false (d) is not valid.

(e) $n (A) \leq n (B) \Rightarrow n (p (A)) \leq n (p (B))$

Let $n (A) = a$ and $n (B) = b$

Then, $n (p (A)) = 2^{a}$ and $n (p (B)) = 2^{b}$ .

Clearly, $a \leq b \Rightarrow 2^{a} \leq 2^{b}$ .

Therefore, $n (A) \leq n (B) \Rightarrow n (p (A)) \leq n (p (B))$ .

Hence, statement (e) is true.

Therefore, the false statement is option (b).

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One of the following sentences is FALSE. Select one: а. - %3D ASAUB O_ b. ASB → ASB ANBSB d. Non of them е. ASB- 9(A)s P(B) Let A and B be sets such that A = 17 and B= 8. The largest possible value of AUB is: Select one: a. Can not be calculated b. 25 C. 8 d. 17 e. Non of them