2. Using the method of full or partial truth tables, say whether the following sentences of L1 are tautologies or not. If not, give a counterexample. (a) ¬(P → Q) → (P → ¬P) (b) (PAQ→ R) → (P → ¬Q V R) (c) (P → (Q → R)) → ((P → Q) → R)

Q: Are the following two sets of coefficients orthogonal? -1, 0, 0, 1 -1, 1, 0, 0 Yes No

A: Given data is as follows: -1,0,0,1 -1,1,0,0 Yes the following sets of coefficients are orthogonal as…

Q: Find AB such that [3 1 21 T-1 A = 2 1 2 and B =|4 [1 2 2] -2 -5]

A: The solution is given as

Q: For which value of x is A = x= 4 1 -4 4 0 0 1 NOT invertible? -3 r

A:

Q: For which value of x is A = x = 4 1 -4 4 0 -3 0 1 x NOT invertible?

A: The objective of this question is to find the value of x for which the given matrix A is not…

Q: d) If A is invertible and AB = 0 then, B = 0.

A: we are given that A is invertible and AB=0

Q: Determine whether the following are linear trans- formations from R³ into R²: (а) L(x) 3 (х2, хз)"…

A:

Q: Compute the following: (1) C(6,4)= (2) C(7,5)=   (3) C(9,5)= (4) C(8,3)⋅C(8,5)=

A:

Q: a) Suppose g then f is "b) a Supnose

A: (a) Given that, g : X to Y and f : Y to Z are functions. It is also given that, f o g : X to Z is…

Q: (u + 2)(u – 2)(u² + 4)

A: Given expression, u+2u-2u2+4

Q: Let a = (1,2, 3), b = (1,0, –1) and c = (2, 1, 3). (a) Verify that a · (2 b+c) =2(a · b) + (a · c).

A: a=(1,2,3) , b=(1,0,-1) and c=(2,1,3)

Q: Show that (u×v)· w = u ·(v×w).

A: As we know that, Multiplication is an Associative Property, i.e. (a x b).c=a.(b x c) and Sometimes…

Q: (b): Evaluate: SS (16t³ – 12t² + 5)dt

A:

Q: Find the L(e2" (1+ t)²). ,2t a) + (s-2)* 1 b) + (s-2)2 2 (s-2)3 (s-2)2 c)+2 (s+2)³ (s-2)? d) +…

A: The following formulas can be used to obtain the Laplace transform.…

Q: Give an example of C = diag(c1, C2, C3) and D = diag(dı, d2, d3) where Tr(C) det(D), but C is not…

A:

Q: P(A)=0.02 and p(C)=0.07 determine p(A u C), given that A and C are independent

A: It is given that:And, A and C are independent events.

Q: (c) Check whether or not: Q (2¹/³) = Q(4¹/3) Also obtain (Q (2¹/³): Q].

A: We first find [Q(2^(1/3)):Q]  Then using this prove that Q(2^(1/3))=Q(4^(1/3))

Q: 6 - 1 2 Compute A - 31I, and (312 )A, where A = - 5 4 - 5 - 3 1 2

A:

Q: Determine whether (p→q)→(q→r) is equivalent to q→r. Justifyyour claim.

A: we have to check whether  (p→q)→(q→r) is equivalent to q→r

Q: 3. Show that B = {0, 1, 2, 6, 9} is a difference set in Zjj. What are the parameters of the SBIBD…

A: For the given question ,t he first thing to do is to find the value of λ. Then, we will proceed…

Q: Determine the minimal polynomial of 2/3 – V5 ov over 0.

A: That's easy. Have a great day!!!

Q: What’s (E∩F)×(F∪G)

A: We are given that E = {1, 2}, F = {2, 3} and G = {3, 4}.Now, E∩F = {2} and F∪G = {2, 3, 4}.

Q: Compute 5f – 7g, given that f(r) - and g(z) - e. -1) "(z-1) Se

A:

Q: T 8-1 H = 2 1 & T = 6 5 Find T TB] (NO guess and check on linear combinations!)

A:

Q: Determine the simplified form of (4 – 37) (–9 + j) – (8 – j5).

A:

Q: If v = -2 4 and w = 4 11 3 " compute proj(w) and proj(w).

A: (.) Given vectors are,      (.)  If  are two vectors then,         (.) Vector  is an orthogonal…

Q: Prove Equationally that A → BF¬B → ¬A.

A: let us check whether the given statement is true or not

Q: Are the following graphs isomorphic? Justify..

A: We clearly see that the first graph, say G1 contains two 3-cycles [one the smaller inside and the…

Q: Verify that (AB)T = BTAT.

A:

Q: Q2. Find the inverse of 2 1 1 0 1 0 5 4 1 3 if it exists.

A:

Q: Question 16 Evaluate: (A +C 글지(Sx + 3) +C В C 2x D x++x ]+C

A:

Q: 2. 5. 2.6= 3 and c = 5. Let a = %3D 3 Compute (1) a + c (2) a + 6+ a (3) c+d +b

A:

Q: Let A = {a, b}, B = {x, y}, C = {x, z}. а) (6.1 #32b) Find P(A x B). a

A:

Q: LetP(A) = 0.20, P(B) = 0.80, andP(A∩B) = 0.16. Are A and B independent? Justify your result…

A:

Q: A group of 90 tourists has a trip in Boracay. The island has two kinds of vehicle, the ordinary…

A:

Q: Are the following statements TRUE or FALSE? e  is a rational number. _____________   2. Every…

A: Consider the provided question, (1) e is rational number, true or false. Since, a rational number is…

Q: 1: = 2 -1 1 2 4 1-3 5-2 1 3 4-2 5 -2 1 3 3 -1 4 -1 2-4-2 7 2 - 4 P = 90 3 4 1 0-45 0 0 0 18 90 90…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts which…

Q: Suppose (x1,x2) + (Y1,Y2) is defined to be (x1 + Y2 ,x2 + Y1). With the usual multiplication cx = (…

A: It is given that the addition is defined as x1, x2+y1, y2=x1+y2, x2+y1 and the multiplication is…

Q: Evaluate ㅠ (2) 풍 1 1 5 -dt. t² + 1 (b) ㅠ 24 (c) 쯔3 (d) ㅠ 2

A:

Q: Let à = (0, 3, 2), b = (3, 1, 1), and c a = Compute the following: (à. b) (à. c) (à. b) e a. (b + c)…

A: