# disprove

1. ### Vector Calc - Prove/Disprove

Prove or disprove that if del dot F = 0 and del x F = 0 then F is a constant vector field. I know that F is a conservative vector field if del x F = 0, but beyond that, I'm really not sure how to approach this problem.
2. ### Prove or Disprove

Prove or disprove: If a is congruent to b (mod m) and b is congruent to c (mod m), then a is congruent to c (mod m).
3. ### Prove or Disprove the following statement

if x is a real positive number then x + 16/x >= 8 I'm having trouble coming up with the start of the proof. Any assistance is appreciated.
4. ### prove or disprove for sets A,B,C

prove or disprove for sets A,B,C A \cup (B-C) = (A \cup B) - (A \cup C) I drew a venn diagram, I believe its false, because on left hand side an element can be in in the intersection of A and C and still be out of B-C. is that correct?
5. ### Prove the following statement: If r3 is irrational, then r is irrational. disprove

9. a. Prove the following statement: If r3 is irrational, then r is irrational. (by contrapositive) b. Disprove the converse of the statement in part (a). a) let r be rational number r=\frac{a}{b} for a,b \in \mathbb{Z};b \neq 0 r^3=\frac{a^3}{b^3} a^3r^3=b^3 \rightarrow...
6. ### prove or disprove: The difference of the squares of any two consecutive integers is

prove or disprove: The difference of the squares of any two consecutive integers is an odd integer Let m, n and p be any integers such that m and n are consecutive and Let m^2 - n^2 = p. if m > n, then by definition m=n+1. Because m and n are consecutive integers neither are both even nor...
7. ### Prove or disprove

I need help on this problem: Prove or find an example to the contrary. There are no complex 3x3 matrices X and Y such that XY-YX= $$\left[\begin{matrix}1&0&0\\0&-2&0\\0&0&3\end{matrix}\right]$$ I don't know how to start. Please, help
8. ### Prove or disprove that two angles are equal in a quadrilateral

A quadrilateral ABCD with mAB=mCD, where m means measure or length. mAD < mBC. E is the middle point of AD. F is the middle point of BC. G is the middle point of BD, H is the middle point of AC. Prove of disprove that angle of GEF must egual angle FEH. The points are below...
9. ### Prove or disprove the following statement; modulo, variables, integers, etc.

I am working through a past exam as part of my study for uni, and I've come across a question that I can't work out. Prove or disprove the following statement: For all intergers n, 3(n^2)-5 is either congruent to 2 modulo 4 or congruent to 3 modulo 4. I really don't even know where to start...
10. ### Algebraic structures - help with prove or disprove question

Hi. I need to prove or disprove the following: 1. Let B=\left \{ s+tx|s,t\in \mathbb{Q} \right \} and A=B\setminus \left \{ 0+0x \right \}. A is a Group. 2. Let B=\left \{ s+tx|s,t\in \mathbb{Z}_5 \right \} and A=B\setminus \left \{ 0+0x \right \}. A is a Group. both with the operation...
11. ### How to disprove that all numbers A1,A2,A3, A4....An are less than their average?

Its something very simple yet I cant figure it out. I know that if all a are smaller than their average, then you can show that this average is smaller than itself. But how to actually do that? I'm new to Discrete Mathematics and am having a hard time so please help me out. Thanks
12. ### prove or disprove the following. let a1....ar be even integers and let b1....bs be in

prove or disprove the following. let a1....ar be even integers and let b1....bs be integers. If r>=s+3 and ai>bj for all i and j, then the quotient (a1a2...ar)/(b1b2....bs) is either an even integer or a non-integral rational. please need an elaborate answer. quickly
13. ### How do you generally prove (and disprove) If-then theorems?

Suppose a theorem proposes If P then Q. Are the only two ways to prove that the If-then statement is true is to show that for any P, Q must be the consequent? I've heard that another way to prove that the statement is true is to show that for any ~Q, the consequent must be ~P. That is, if we...
14. ### prove or disprove question about two natural number

prove or disprove : for all M, N in natural number , M < N => (exists some number K in natural number ,such that M < K and k < N) I notice that this is a false statement which i need to proof the negation of statement to disprove it. so far i got , for all M , N in natural number , M < N =>...
15. ### prove or disprove

for all x,y in Real Number , that x > y , then there exists a number Z , such that x<z and z < y. I concluded this is a false statement because the inequality would be Z > x > y > Z which make no sense, but how to disprove this?. please help~
16. ### prove or disprove: sup of two sets

Hi, i need to prove or disprove the following: Sup(A\cup B)=max\left \{ SupA, SupB \right \} thanks in advanced! *edit: both sets are bounded from above.
17. ### prove or disprove: statement about Span

V is a linear space. A,B\in V are sets, and W is subspace: Span(A\cup B\cup W)=(Span(A)+Span(B))\cup W i just need help to figure out if it's true or false. thanks in advanced!
18. ### prove or disprove: statement about Span

Hi. is this true or false: Span\left \{ u \right \}=Span\left \{ u,v \right \}\cap Span\left \{ u,w \right \} u\neq 0 Thanks in adnvanced! BTW, i think it is true, but i'm not sure...(Worried)
19. ### prove or disprove

Prove or disprove: if x and y are real numbers with y ≥ 0 and y(y+1) ≤ (x+1)^2, then y(y − 1) ≤ x^2.
20. ### propositional logic: prove or disprove

i'm supposed to prove (p → q) ∧ (¬p → r) ⇒ (q ∨ r) with a truth table and im stuck. i've created most of the truth table by hand. but i do no know how to prove or disprove it. any help is much appreciated.