Recent content by sonadoramante

Former humanities/arts guy that is transitioning into computer science, namely software development. I am also fond of mathematics but merely as a hobby. Currently pursuing a degree in computer science at a university in North America. It feels great to be a part of this awesome & supportive...

Thanks a lot.

After feedback. Let p be a even integer & q be any positive integer. Given that even number*even number is even & even number*odd number is even, then.. p=2m pq= 2mq pq= 2(mq) Let k=mq pq=2k Hence pq is even. :)

No! My bad. It didn't specify in the question that a is positive.

It wasn't specified, however, I was trying to prove it for both cases (if b is even or odd positive integer)

Aha! That makes more sense. a+b = 2n+1+2m+1 = 2n+2m+2 = 2(n+m+1) = 2k Hence a+b is even. :)

Proof: Let a be a even positive integer of the form a=2m & b of the form b=2n (This is where b is a even positive integer) ab = 2m*2n = 2(mn) = Let k = mn = 2k Therefore, ab is even. Let a be a even positive integer a=2m & b be a odd positive integer b = 2n+1 ab = (2m)*(2n+1)...

Summary:: Prove that if a is an odd integer and b is an odd integer then a+b is even. Theorem: If a is odd and b is odd then a+b is even. Proof: Let a and b be positive odd integers of the form a = 2n+1 & b = 2m+1 a+b = 2n+1+2m+1 = 2n+2m+1+1 = 2n+2m+2 = 2(n+m)+2...

@pbuk It was one of the practice problems (without the solutions provided) from "how to prove it" for our discrete mathematics class.

You're right. It is inclusive (OR)

Yes! We use inclusive (OR).

Makes perfect sense! Thanks.

Commutative property of addition. If a & b are integers then, a+b = b+a 2+3 = 3+2 5. Does not work for subtraction. 2-3 = -1 3-2= 1 Having said that, what about the special case with negative numbers (when we also move their respective signs) -5 + 7 = 2 & 7 + (-5) = 2. 15 -7 = 8 & -7 + 15...

Thank you! J= John is telling the truth. B= Bill is telling the truth. S= Sam is telling the truth. J v B ~S v ~B ------------ Therefore, J v ~S J B S J v B ~S v ~B J v ~S F F F F...

Let P stand for John is telling the truth. Let Q stand for Bill is telling the truth. Let R stand for Sam is lying. P v Q R v Q ----------- Therefore P v R P Q R P v Q R v Q P v R F F F F F F F F T...