Either prove the wff is valid or give an interpretation that is false: (p.71) 18. (EEx)[R(x) V S(x)]-> (EEx)R(x) V (EEx)S(x) 28. (AAY)[P(x) V Q(x)] A (EEx)Q(x) -> (EEx)P(x)

Q: 2) Show that 2m +1 m P(x) m +1 -xP (x) m+1 (x)F

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Q: 8) For f(x) = x +1 and g (x) = 5x + 4, determine the following. a) 4 points h (x) = (f •g)(x). b) 4…

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Q: Use proof by contradiction approach to prove that VxM) V N(X)

A: This is a problem of Predicate Logic.

Q: 4) [ (2– t)/tdt xdx 5) o Jr+ 2x 2

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Q: 7. Translate these statements into English, where C(x) is "x is a comedian" and F(x) is "x is funny"…

A: Introduction: The free variable b of the ∀:right and ∃:left inferences is known as the eigenvariable…

Q: For each statement, either prove that it is true or come up with a counter example N(ATA) = N(A) ● •…

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Q: Given that P(X)= P(Y)= and P(XUY)= find 20 20 10 a) P(XnY) b) P(XIY)

A: Given,PX=920PY=720and PX∪Y=710

Q: 4. Use rule of inference to show that if Vx(P9x) → (Q(x) ^ S(x))) and Vx(P(x) ^ R(x)) are true, then…

A: Given: Lets determine∀xPx→Qx∧Sx and ∀xPx∧Rx is true and ∀xRx∧Sx is true using rule of interference.

Q: 1 Evaluate using Convolution theorem : L

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Q: 6.- Evaluate T(au + bữ), considering the following 1 T(ī) = 2, T(5) = , T(ī) 2, a = -1 and b = 2 3…

A: T(au+bv)=T(au)+T(bv)

Q: Negate the following statement Vx ay [ (P(x) < QUy)) ^ (Q(x) < P(y))]→ (P(x) = QG))

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Q: rove if the ff. arguments are valid using any formal proof of validity. vx, (P(x) v Q(x)) vx,…

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Q: (b) Let X = {A E Mat2(R) : A is upper triangular} and let Y = {A € Mat2(R) : A is lower triangular}.…

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Q: 3 4 gla) - 4 17 3 A) s '(x) 3 A) Yes B) No -2.x + 8 B) f (x) – 3 C) s '(x) – x – 1 2 3) Sl:) – VI+2…

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Q: Prove the validity of the following arguments Vx, A(x) → B(x) Ex, A(x) ^ C(x) Vx, C(x) →D(x) ..3x,…

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Q: let fAg be funcbions that sabis fy fla)= -4 A g la)=-9. find h'la) for: a) h(x) = 2f(x) c) h(x)= 10…

A: Since multiple sub parts ate asked, I am answering first 3 subparts.

Q: Prove if the ff. arguments are valid using any formal proof of validity. vx, (P(x) VQ(x)) x, (~Q(x)…

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Q: 4 - If a product is sold with 30% profit x TL, if sold with 10% loss, y is TL. So what is 3 (2y /…

A: Given Data: Let C be the cost price x=1.3C y=0.9C

Q: f(x) = 2x – 15 g(x) = /2r h(x) = j(x) = -(2x)2 12. (f +g+h+D(1) 13. (h+ )(x) 14. h(g(81))

A: Here we are given fx=2x-15, gx=2x, hx=32x, jx=-2x2 We have to find  (f+g+h+j)(1) , (h÷j)(x) ,…

Q: 4. Let f(x) = g(x) = x -5, k-(10) +7 = 10 and h (x) = find: ther b. Domain of h(x). c. (hof)(2). (Z…

A: (NOTE:   As nothing is mentioned, so all functions are taken as real valued functions.)

Q: If f f(x) dx 2 and g(x) dr 5 what is 2f(x) +g(x) dæ? 0 4 O 11 13 0 7

A: Let ∫abf(x)dx=m and ∫abg(x)dx=n then ∫ab[af(x)+bg(x)]dx=am+bn

Q: 2) Let T [ ] = DT [₁2 i] = i) 0 ii) 2T = 1 + (-c-d)x+ (-d)²x² + (a + c)³ x³. Then we have: -7 - =

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Q: Michelle draws a restangle with a length of 6 cm. She draws a second rectangle with a length of 11…

A: Michelle draw 1st rectangle of length =6 cm 2nd rectangle=6+5=11cm And so on, she keep drawing more…

Q: I(¥x (P(x) v Q(x))) ^ (Vx (¬Q(x) v S(x))) ^ (Vx (R(x) → ¬S(x))) ^ (3x ¬P(x))] → 3x ¬R(x)

A: Given: To do: Prove the above statement.

Q: (3x)[R(x) V S(x)]→(3x)R(x) V (3x)S(x)

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Q: Q2) If f (x) = x + 5 and g(x) = x² – 3, find the following: %3D 1) f(f(x)) 2) g(f(x)) 3) f(g(x)) 4)…

A: Given that: f(x)=x+5          and    g(x)=x2-3

Q: let x be have P.dif 0 < x <3 f(x)= ={th find The U.b. of P(IX-M73) and find The L. b.

A: Please see below

Q: 3) 4) Find g(3) for g(x) = √-x5. Find p(-x) for p(x) = x³-√1-x .

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Q: *) Let p(x) = 8x – 7 and q(x) = /x – 7. Find u(x) given that q(x) = p(u(x)). - и(x) —

A: see 2nd step

Q: (1).p^(p→q)^(-qVr) →r

A: We shall solve first question only as you have asked more than one distinct questions. For others…

Q: 21. Let V1 = 1 0 -1 V2 H " V3 = 0 {V1, V2, V3} span R4? Why or why not? 1 0 0 . Does

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Q: Disprove: X={r1, 12} iff V, (z E X +x=VI=T2)

A: To do: Disprove the statement…

Q: Which of the following statements is correct? a) P(X | Y) = P (X) if X and Y are independent.

A: Our aim is to find the correct statement.