prove

1. Proving the Cardinality of 2 finite sets

Hi all! This is my first post, and my partner and I have struggled to try to understand the following optional/suggested problem: Let A and B be finite sets. Prove that |A - B| = |A u B| - |B|. In words: "Prove that the absolute value (or cardinality) of A minus B is equal to the absolute value...
2. Prove question - needs algebra

Prove that squaring a number will give a number that is divisible by 4 Sorry I meant to put even number that will be divisible by 4
3. how to prove domain of polynomial

Hi; How do you go about proving the domain of a polynomial function? I know its domain is (-infinity,infinity) but how do I prove this given a function? Thanks.
4. how to prove multiplicative integers (mod p) has at least one generator?

How do you prove the multiplicative integers (mod p) has at least one generator? I know how to show a^(p-1) is congruent to 1 using Fermat's Little Theorem but how do you show p-1 is the smallest such integer? Thanks!
5. prove surface area of sphere

I 'm having problem of proving the total surface area of sphere = 4pi(a^2) , in my workin g, i got surface area = 2pi(a^2) only .... I 've checked it many times , still cant figure out which part i'm wrong... P/s : the sphere has radius of a .
6. How to prove

Hi, I want to learn the art of constructing proofs but it proves difficult namely because I don't know how to begin. I've become familiar with a variety of methods such as proof by contradiction, deduction, exhaustion, induction etc. How I approach trying to prove something is that I read it...
7. Steep Diagonals and Magic Squares - Prove and State a Theorem

[/FONT] [/CENTER] [/TD] We want to describe via a picture a set of subsets of a square which are something like diagonals, but are not quite the same. We’ll call them steep diagonals. One of them, labelled e, is illustrated in the square below; the other 6 are parallel to it. State and prove a...
8. prove the equation

can someone explain why the author cancel off both circled part directly ? for the circled part , only the numerator are same which is sin(n pi) , but the denominator are not the same ! why the author wanna do so ?
9. Prove Identity

I've tried starting from both sides, using sin and cos double angle formula, but I seem to be getting nowhere. Please could someone outline the steps.
10. If p>5 and 2p+1 are prime, prove that 3|4p+1

a.) Suppose that p>5 is prime and 2p+1 is also prime. Prove that 4p+1 is a multiple of 3. b.) Assume that p>5, 2p+1, (4p+1)/3, and 8p+1 are all prime. Prove that p is congruent to 29 (mod 30). I'm totally stumped. Any help would be greatly appreciated.
11. can anyone help me prove this?

If a , b and c are real numbers such that a ≠ 0 and b2 > 4ac, then there exists two distinct real number u and v that u + v =-b/a and uv = c/a.
12. Prove that sinA sinB <= sin^2(C/2)

Question : In a triangle ABC, a point D is so taken on side AB such that CD^2 = AD·BD Prove that sinA·sinB <= sin^2(C/2) Discuss the case of equality. My attempt : I used Apollonius' Theorem to get -> a^2 + b^2 = 2(BD)c {where a, b, c are sides opposite to angle A, B, C respectively in...

17. Prove using these laws without truth tables?

Can someone explain to me in detail how to complete these two problems without using truth tables? I'm having a hard time understanding what to do. I know that I'm supposed to use the laws, etc. But I'm confused on this entirely. Prove that ((p → q) ∧ ¬q) → ¬p is a tautology without...
18. Prove that large number is a multiple of 7 using modular arithmetic

How can you show that 3^54321 - 6 is a multiple of 7? I know you would use modular arithmetic (and maybe the Euclidean algorithm?), but I don't know how to go about doing that. Any help would be greatly appreciated!
19. Prove function is a homomorphism

Let G be a group. Fix g ∈ G. Define a map φ : G → G by φ(x) = gxg^−1 Prove: φ is an isomorphism What I Know: I already showed it is bijective. Now, I need help proving the homomorphism part. I know by definition for all a,b in G, f(ab)=f(a)f(b), Question: How do I show this? For some reason I...
20. prove q are not complete

From the definition : Q is complete iff every non empty bounded from above,subset of Q HAS A sUPREMUM IN Q,WE CAN INFER that Q is not complete: if there exists a non empty,bounded from above subset of Q that it has no Supremum belonging to Q. So the main idea is to find a non empty ,bounded...