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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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
Transcribed Image Text: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 A¯=nA

To determine the false statements.

(a) nA≤nA∪B

For any sets A and B, A⊆A∪B.

Then, clearly, nA≤nA∪B

Therefore, the statement (a) is true.

(b) nA≤nB⇒A⊆B

Consider two sets, A=1, 2 and B=3, 4, 5.

Here, nA≤nB but A is not a subset of B.

Therefore, nA≤nB⇒A⊆B is not true.

Hence, the statement (b) is false.

Step 2

(c) nA∩B≤nB

By definition, A∩B⊆B.

Therefore, nA∩B≤nB.

Hence, the statement (c) is true.

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

(e) nA≤nB⇒npA≤npB

Let nA=a and nB=b

Then, npA=2a and npB=2b.

Clearly, a≤b⇒2a≤2b.

Therefore, nA≤nB⇒npA≤npB.

Hence, statement (e) is true.

Therefore, the false statement is option (b).

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