T(n)= 3T(n/2) +5 is (noga (3))

Set ProofsProve or disprove the following claims.

Looking for help on this question: Use the following building blocks in the right column to assemble a direct proof that the product of two odd numbers is odd. Not all blocks belong in the proof.

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Part 1: Choose two of the proofs below and use one of the indirect proof techniques (reductio ad absurdum or conditional proof) presented in Chapter 8 to demonstrate the validity of the arguments. The proofs below may use any of the rules of inference or replacement rules given in Chapter 8. 1.(G • P) → K, E → Z, ~P → ~ Z, G → (E v L), therefore, (G • ~L) → K 2.(S v T) ↔ ~E, S → (F • ~G), A → W, T → ~W, therefore, (~E • A) → ~G 3.(S v T) v (U v W), therefore, (U v T) v (S v W) 4.~Q → (L → F), Q → ~A, F → B, L, therefore, ~A v B 5.~S → (F → L), F → (L → P), therefore, ~S → (F → P) Part 2: Below are basic arguments in English. Choose two arguments and translate those argument into the symbolism of predicate logic. You do not need to do a proof. Every fetus has an immortal soul. A thing has an immortal soul only if it has a right to life. Hence, every fetus has a right to life. (Fx = x is a fetus, Sx = x has an immortal soul, Rx = x has a right to life). Some wars are just. No war of…

Determine the validity of the following arguments using truth tables. Which confluence of truth values shows its invalidity? 1. A ⇒BB ⇒A -----------∴A ⇒B 2. (E ∨R ) ∧(E ∨T)R ∧T ------------∴E 3. (O ∨P) ⇒JO ∨¬JP ∨¬JO ⇔¬P -----------∴J ∧¬J

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2) Consider the expression xz' + xy + yz' = (x+z)(y+z') Use perfect induction to prove/disprove this relationship.

Determine whether the following statements are true or false. Justify your answer with a proof or a counterexample. a. For all integers , a,b,c  if a I bc then a I b or a I c   b. Determine the prime factorization of 44,574.