12. Write down the contrapositives:
(a) If two rectangles are congruent, they have the same area.
(b) If a triangle with sides a, b, c, is right-angles, then a^2 + b^2 = c^2
(c) If 2^n -1 is prime, then n is prime.
(d) If the Yuan rises, the Dollar will fall.
13. Use truth tables to show that the contrapositive and the converse of A => B are not equivalent.
14. Write down the converses of the four statements in question 12.
Contrapositives. Work on some more of this tomorrow. (If I am tired, I am going to bed. I am tired, therefore I must be going to bed.)
ReplyDelete(a) If two rectangles do not have the same area, they are not congruent.
(b) If the measurements of the sides of a triangle do not satisfy a^2 + b^2 = c^2, the triangle is not a right triangle.
(C) If n is not prime, then 2^n-1 is not prime.
(d) If the dollar does not fall, the yuan will note rise.
OK, while I am at it, I will do the converses.
ReplyDelete(a) If two triangles have the same area, they are congruent. (This is not a true statement, by the way.)
(b) If then a^2 + b^2 = c^2, the triangle must be a right triangle.
(c) If n is prime, then 2^n-1 is prime.
(d) If the dollar falls, the yuan will rise
When going through the lecture on this, I thought of the example, "If I am a mother, I must be a woman." The contrapositive says, "If I am not a woman, I am not a mother." Ignoring a more modern definition of "mother", this is true. But the converse is not: "If I am a woman, I must be a mother." Definitely not true.
13. I won't bother with the P and Q columns.
ReplyDeleteP->Q Q->P
T T
F T
T F
T T
Therefore, non-equivalence.
Thanks for the nice countrapositive/converse "motherhood" example, Diane.
ReplyDeleteHow about this as a countrapositive:
a) I can't read a lot of those damn Captcha images, so I must be over 40.
b) If I am not over 40, I can read those damn Captcha images.
Anyway, let me try to read another one so I can publish this. :-)
Ha! I squint at those, too. Guess I'm over 40...
ReplyDelete