b) Prove or disprove that if n2 43n +5 is even then n is even. Isubivibni od Jaum loo1g

Q: п(n + 1)(n + 2) 4. If n e N, then 1.2+2.3+3·4+4·5+...+n(n +1) = 3

A:

Q: 11. If an+1 = 2an + 3 and ao = 1, then a7 = O 513 O 509 O 487 496

A: We will find a7.

Q: ve that the only perfect number of the form n = p²q where p and q are distinct primes is 28.

A:

Q: (1) Give a proof by contradiction of the statement: If n? + 3n – 5 is even, then n is odd.

A:

Q: Prove that if n is an integer and 7n+2 is even, then n is even. State which method you are using for…

A: Let  n be any integer.  We have given that , 7n + 2 is even. We need to prove that ,  n is even. We…

Q: 3. Show that √2+√3 is irrational. Show that √n-1+√n+1 is irrational for every integer n ≥ 1.

A:

Q: Suppose N = Fox F₁x F2, where the three factors are pairwise prime; hence, each factor and the…

A:

Q: Multiply (3x-2X2x+

A:

Q: Prove that p=5 and q=2 are the only pair of prime numbers such that p−q=3.

A: you can solve it by using the solution of Diophantine equation. So , Here we have to prove  p = 5…

Q: 5. Prove that (n, n + 2) = 1 is n is odd and (n, n + 2) = 2 is n is even.

A: Suppose (n, n+2) = d => d | n and d | n+2 => d | (n+2) - n => d | 2 => d = 1 or 2.

Q: 10. Let a and b be natural numbers that are co-prime. Prove that (b-a) and b must also be co-prime.

A:

Q: Which choice gives an example that supports the conjecture, and a counterexample that shows the…

A: The objective is to select the correct option from the given options. Given that, for any real…

Q: If n ( A ) = 25 , n ( B ) = 40 , a n d n ( A ∪ B ) = 55 ,what is n ( A ∩ B ) ?

A: Consider the given information nA=25,nB=40and nA∪B=55

Q: Exercise 1. A student is asked to prove If m is even and n is odd, then m² + n² is odd. 2 The…

A: Let us answer above questions

Q: 5. Prove that (n,n+2) = 1 is n is odd and (n, n + 2) = 2 is n is even.

A:

Q: It is a fact that if n is any nonnegative integer, then 1-(1/2"+1) 1 1 1 1+=+ + + •+ 2 2² 23 1-(1/2)…

A:

Q: Consider the following statement. There is an integer n such that 2n² - 5n + 2 is prime. To prove…

A:

Q: Suppose n E Z. Prove that if n is even, then n² + 7n + 10 is even. (Use Direct Proof)

A: Suppose that n∈Z and let n is even.To show: n2+7n+10 is also even.

Q: Prove that 74n+3 + 2 is a multiple of 5 for all non-negative integers n.

A:

Statements and Logic

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