n ∈ Z, d ∈ N} and define (a, b) ≡ (c, d) to mean ad = bc 1. For any (n,d) we have (n,d) ≡ (n,d) 2. If (a,b) ≡ (c,d) then (c,d) ≡ (a,b) 3. If (a,b) ≡ (c,

Q: If A × B ={(p, q),(p, r), (m, q), (m, r)},     find A and B.

A: A will be the set of the first ordinates  And B is the set of the second ordinates

Q: Let A=(1, 0), B=(0, 1), C=(1, 1), and D=(r, 1). Verify that R(A, B, C, D) = r.

A:

Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

A:

Q: 10. Find a and ẞ such that c = αa + ẞb, where a = (-3,0,2), b = (0,-1,2), and c = (-6,5,-10).

A:

Q: = (-10,6, –4) be in R and a be in R. Then , 36 , Let x ат — ).

A:

Q: If P(n-1,3):P(n,4) = 1:9,Findn.

A:

Q: If n(A) = 46, n(B) = 19, and n(AN B) 19, and n(An B) = 4, find n(A U B).

A:

Q: 10.

A:

Q: If a = (2, 0, 2), b =(4, 2,-2), and c = ax (bx c) = (a x b) x c = = (0, 2, 5), show that a x (bx c)…

A: The answer is in step2.

Q: リ ー上 5, Use the inverse imatirice s tofind and (24) 22 3 ミ 3. 3. 3 -2

A:

Q: A = 2 1 2 0 1 -H B = W = w-B Find the following: a- A², AB, det(A) b- If AW=B, find (W) using…

A:

Q: Prove that A-B=An(-B) = (-B) – (-A) = −[(-A) U B]. Also, give three expressions for An B and AU B,…

A: Difference of sets: Given two sets A and B, the difference A−B is defined as the set of all elements…

Q: Let A={2,y,z} and B={3,x,z}. How many distinct elements are in (A×B)∩(B×A)

A: Given, A={2,y,z} B={3,x,z} How many distinct elements are in (A×B)∩(B×A) ?

Q: If u x = [1, -3,5], thenx =

A:

Q: If ~v = 〈 4, 1, 6〉 and ~w = 〈3, 2, 3〉, find ~v · ~w and ~v × ~w.

A: If ~v = 〈 4, 1, 6〉 and ~w = 〈3, 2, 3〉, find ~v · ~w and ~v × ~w.

Q: 9. Given u =(2,-2), v = (5,8), and w = (-4, 3), find each of the following. (a) u v (b) (u - v)w (c)…

A: