1. a. Using inductive reasoning, show that t(n+ 1) = t(n- 2)+ 2t(n- 1). t(1) = 1 t(2) = 1 t(n) = t(n- 2) + t(n- 1) for n= {2, 3, 4, ...} t(n+ 1)=t(-2) +t This is the recursive formula. 0-1) Replace n with n+1.

Q: (1) Use quantifiers, logic symbols, and English to translate the following: (a) Every positive real…

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A: Let A and B be two sets , then  n(A∪B)=n(A)+n(B)-n(A∩B) . Given that n(B)=5 and n(A∪B)=7 .

Q: t + 4 Let p(t) 12 – 2t Evaluate p(3): p(3) t 3= Determine t when p(t) 2

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Q: otal points 13. Construct the sign diagram for the expression (x + 1)(x - 2). O O I (x + 1)(x - 2) O…

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Q: Question ( 27)/(50) 7 The coeffiecient for 6m+7 is m A False B True

A: Given query is to find the statment is true or false.

Q: 2. (a) Show that for all integers n ≥ 0,32n-1 is divisible by 8. (b) Show that 2n -1. (d) Show that…

A: Let's go through each part one by one:(a) Show that for all integers  is divisible by 8.It can prove…

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Q: Prove that: n n (3) + (-²)=(-+ m m+1 n+1 m+1

A: We have to prove the given identity

Q: 3. (a) If etB and eta are both contractions on R", and BA is a contraction. Similarly for…

A: We  have  first recall  the definition of contraction map.Let   be a  function.Then,   is  said  to…

Q: Find the 25th term of : 2, -10, 50, .. Selected Answer: (2) + (25 – 1)*(-5) Answers: (2) + (25 -…

A: Given: The sequence of terms is provided as: 2, -10, 50, ……                             The 25th…

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A: Put a pair of brackets on the left hand side to make these statements correct

Q: -3an The solution of the recursion relation an+1 = n > 0, is an = 2(n+1)? " a) None of these Ob)…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.