Answer
a. R(25, 10) is: "If 25 is a factor of 100, then 25 is a factor of 10." The hypothesis (25 is a factor of 100) is true, but the conclusion (25 is a factor of 10) is false. Therefore R(25,10) is false.
b. Let m=36 and n=6. Let m=24 and n=12. Let m=25 and n=15.
c.R(5,10) is: "If 5 is a factor of 100, then 5 is a factor of 10." The hypothesis (5 is a factor of 100) is true, and the conclusion (5 is a factor of 10) is also true. Hence R(5,10) is true.
d. Let m=5, n=25. Let m=3, n=9. Let m=4, n=12.
Work Step by Step
b. Q(36, 3) is: "If 36 is a factor of 36, then 36 is a factor of 6."
Q(24, 12) is: "If 24 is a factor of 144, then 24 is a factor of 12."
Q(25, 15) is: "If 25 is a factor of 225, then 25 is a factor of 15."
In all the above cases the hypothesis is true but the conclusion is false. For any x, y, if x>y, x cannot be a factor of y.
d. Q(5,25) is: "If 5 is a factor of 625, then 5 is a factor of 25."
Q(3,9) is: "If 3 is a factor of 81, then 3 is a factor of 9."
Q(4,12) is: "If 4 is a factor of 144, then 4 is a factor of 12."
In each of the cases both the hypothesis and the conclusion are true.
