Let m, n, d₁, and d₂ be integers. Show that if d₁m and d₂|n, then d₁d₂|mn.

Q: З and an - - 3ап-1 + an-2 for integers n>2. Evaluate and d4: Let a, = 2, a2

A:

Q: 3. Let A = {1, 2, 3}. What is |A|?

A: If A = {x,y,z}  |A| = sqrt x^2 + y^2 + z^2

Q: Let a, b e R. Prove that if 15a + 206 = 49, then a and b are not both integers.

A: we have 15a+20b =49 and a and b both are in R  we prove that a and b are not both integers.

Q: Let a and d be integers. Prove that if d|(8a+7)and d|(5a+4), then d|3

A:

Q: Evaluate dz. 23 x2+1

A:

Q: Let 4; = {0, i} . Find U4, and N 4. i= 1 | A;. i= 1

A: Given :  Ai =  0 , i    To find :  The union ∪i=1∞ Ai    and the intersection  ∩i=1∞ Ai   .

Q: antip . Prove that 4" -3"-7 is a multiple of 84 for each positive even m.

A:

Q: dx. Evaluate - 1)²(x² + 2) x+3

A:

Q: 8. Let dgcd(135, 351). Find integers m and n such that 135m + 351n = d.

A:

Q: Prove that A2=I.

A:

Q: Determine whether the statement is true or false. Prove the statement directly from the definitions…

A: a. For all integers a,b, and c, if a | bc, then a | b or a | c.To demonstrate this assertion, we'll…

Q: S[e²t. √4+e²] dt

A: Evaluation of the indefinite integral, by using substitution method

Q: 2. Show that for all positive real numbers a and b, if a < b then a² < b².

A:

Q: let a b c and d be integers, prove if a|b and c|d then ac|bd

A:

Q: Let a and b be integers. Prove that GCD(a,b) divides GCD(a+b, a−b). Give an example when GCD(a,b)…

A:

Q: Suppose that p is false, but q is true. Which of the following statements are also true? Select all…

A: Given the statement p is false, but q is true.

Q: Let u=(9,−8)​, v=(1,9)​, and w=(−2,7). Carry out the following computation. Find u+v+w.   |u+v+w|=?

A: Given that  Let u=(9,−8)​, v=(1,9)​, and w=(−2,7) To Find u+v+w.

Q: Let a, b be nonzero integers with (a, b) = 1. Compute (a + b, a – b).

A:

Q: If 2ª = 3b then =? O 1.4 O 1.5

A:

Q: 9. Let a, b, and d be positive integers. Prove that if (a, b) = 1 and d divides a, then (d, b) = 1.

A:

Q: . If n(A) = 30, n(B) = 40, and n(A ∪ B) = 45,find n(A ∩ B).

A:

Q: Show that AB = O, even though A ≠ O and B ≠ O.

A:

Q: Suppose that P(A) = 0.4, P(B) = 0.3 and PAUB)-042, then a. A and B are dependent b. none of the…

A: We have to find out correct answer...

Q: Find the product of x and y if x, 3/2, 6/7, y  are in G.P

A:

Q: Let a, b, and c be integers with a 0. Prove that if a | b and a | (b + c), then a | c.

A: