Let a,b be two different points in R^n one. We notice that d=(a,b)>0 (why is that so ?). Prove that for all real numbers r1,r2>0 holds: (a) B(a;r1)^B(b;r2)=Ø⇒r1+r2>d (b) r1+r2

Q: Let the domain of x and y be all people, Let W(x): "X is a woman". M(y): "y is a man", and L(x.y):…

A: Given W(x): ' x is a woman' M(y):' y is a man'

Q: Let F= R and V = R*. Let W, = {(x1,x2,X3,X4) € R* : x1 – x2 + X3 – x4 = 0 and x1 +x2 = 0}, W2 =…

A:

Q: For the predicate P(x, y) ::= [x + 2 = y], choose all the pairs of x and y such that P(x, y) is…

A: Given query is to find the correct option for the expression.

Q: Prove that (ab + cd)² ≤ (a² + c²)(b² + ď²) for all a, b, c, d ɛ R.

A:

Q: Give an example where A, B ⊆ X and |A| = |B| but |X ― A| ≠ |X ― B|.

A: This cannot be possible if we take X to be finite set so we have to think an example where X is…

Q: 13. Find the intersection of [x, y, z)=[-8,-3,-5]+[1,2,-1] and [x. v.]=[1.9,4]+s[2,1,7].

A: We can find the intersection of the curve .

Q: Select all the real numbers M among the choices below such that the two planes given by r. -2= -3…

A:

Q: 2. (6 marks) Let a, b, c € Z with a 0. Prove that if a X (a + 2b + 3c), then a Xb or a Xc.

A:

Q: (a) Vx(x² > 4 →x>-2). (b) Vx3y (2x + y² = 0). (c) Vxy(x² + y = 25). (d) 3xy(x² + y² = -1).

A: a False b False c True d False

Q: Show that (a + b)x = ax + bx for all a, b E F and all x € F¹.

A:

Q: Use the equation y = x² - 17x + 72 to answer the following question. For what values of x is y ≥ 0?

A:

Q: Show that if AB={0}, then P(A)≤P(B).

A: Given that

Q: Select all the real numbers M among the choices below such that the two planės glven by 3D2 and ()-…

A: We can solve this by using given information

Q: (h) Vx E R, 3y E R, (x + y > 0 or x + y = 0). (i) Vx E R, 3y E R, (x + y > 0 and x + y = 0). (j) (Væ…

A: .