Prove that 32n + 5 is never divisible by 8, provided that n is a natural number.

Prove that 32n + 5 is never divisible by 8, provided that n is a natural number.

Prove that cos(x)tan(x) / cosec(x^2) = cos(x)^3 / cot(x)^3

My quesiton involves having to be given with statements and reasons.

Let A,B be subsets of a set X. Prove that A is a subset of B if and only if B compliment is a subset of A compliment

Justify your answer with a proof.

Here is what I have so far: The property to prove is R(α). α contains more propositional variables than ∧ connectives. Base Case: α is an atom. α has no ∧ connectives - only a propositional...

For any positive integer n, how do you write a combinatorial proof of the identity (2n choose n) = the summation from i=0 to n (n choose i)*(n choose n-i) ?

prove 1- cos^2 0 = sin 0 cos 0 tan 0

prove the relation sin 0 + tan 0 = tan 0 (1 + cos 0)

Given: ABCD is a parallelogram Prove: Segment AB ≅ Segment CD, Segment BC ≅ Segment AD

I tried minus the right hand side and simplify, but that did not work. I tried simply the left hand side first and even that didint work. Please help! Thanks

1. We are given that diagonals segment AB ≅ segment BD. 2.It can be stated that segment AB ≅ segment DC because they are opposite sides of a parallelogram. 3. By the Reflexive Property of...

1. We are given that diagonals segment AB ≅ segment BD. 2.It can be stated that segment AB ≅ segment DC because they are opposite sides of a parallelogram. 3. By the Reflexive Property of...

Rest of question 3. By the Reflexive Property of Congruence, segment AD ≅ AD. 4. Thus,ΔABD ≅ ____ by the ___ Congruence Postulate. 5. Then ∠BAD ≅ ∠CDA because they are corresponding...

Given: line AB is parallel to line CD and AB is congruent to CD Prove: AE=EC *Note: the diagram given looks like a parallelogram with both diagonals drawn

Hi, I have been asked the following but am struggling. Let {Ωa : a ∈ I} be an arbitrary family of closed sets Ωa ⊆ Rd with an index set I. Prove that ∩ ...

1. The ratio of the volume of a pyramid to the volume of a prism with the same base and height is _____ Because the formula for the volume of a prism is V=Bh , where B is the area of the...

Prove: Triangle CBD is congruent to Triangle CAE Given: angle A is congruent to angle B, Point C is the midpoint of segment AB

What is the proof of that equation? Notice the minus sign instead of plus sign.

Im using a period as dot product and x for cross product. I've been stuck on this problem for a long time. My main question is, if there is a vector next to a parenthesis does that imply cross or...

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