Mathematical Logic And Boolean Algebra Question 63
Question: For integers m and n, both greater than 1, consider three following three statements:
P: m divides n Q: m divides $ n^{2} $ R: m is prime, then
Options:
A) $ Q\wedge R\to P $
B) $ P\wedge Q\to R $
C) $ Q\to R $
D) $ Q\to P $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] b. $ \frac{8}{4}=2,\frac{64}{4}=16; $ But 4 is not prime. Hence $ P\wedge Q\to R, $ false c. $ \frac{{{(6)}^{2}}}{12}=\frac{36}{12}=3; $ but 12 is not prime hence $ Q\to R, $ false d. $ \frac{{{(4)}^{2}}}{8}=\frac{16}{8}=2;\frac{4}{8} $ is not an integer hence $ Q\to P $ ; false
BETA
