Prove or disprove:  For all integers a and b, if a+b is even, then a is even and b is even.

Q: X7. We know that given any real numbers x1 and x2, if x1x2 = 0, then x1 = 0 or x2 = 0. Since there…

A: (b) given any real number x1 , x2 , x3 , x4 claim- if x1x2x3x4=0 then x1=0 , x2=0 , x3=0 , x4=0

Q: Take any arbitrary integer n and then square it, which one is true? n2 cannot be in the form 7k + 5.…

A: Solution is given as follows :

Q: Suppose a and b are both integers that are greater than 1. What is Icm(a, a*b)? a None of the…

A: We have find the lcm of given numbers.

Q: 10 a.) Completely simplify E ()2* i=0 b.) Expand (1 – r)® and simplify. c.) Expand (r +r-1)5 and…

A:

Q: If a is an even positive integer and b is an odd positive integer, then which of the following…

A:

Q: ven ? is a positive integer, prove that ? is even if and only if 5? + 6 is even. You must use…

A:

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

A:

Q: For any integer a, show that a²-a+7 ends in one of the digits 3, 7, or 9.

A: For any integer a , we have to show that a2 - a + 7 ends in one of the digits 3 , 7 , or 9 . Note…

Q: Suppose “a” is an integer. If 5|2a, then 5|a.

A:

Q: AV Prove that every integer greater than 6 can be written as 3x + 4y for nonnegative integers x and…

A: We have to prove that:Every integer greater than 6 can be written as 3x+4y for nonnegative integers…

Q: Let n be an integer, use the definition of even to prove that 10n+ 4 is even. 10n+4=0x0 Since is a…

A: Let n be an integer. To prove that for any integer n the number 10n+4 is even. An even integer is…

Q: Determine which positive integers ? have a. Exactly 2 positive divisors b. Exactly 4 positive…

A: A positive integer has exactly 2 positive divisors if and only if it is a prime number.

Q: Prove or disprove: For all odd integers a and b, 4 | (3a² + b²).

A: We have to prove or disprove the given statment.

Q: Prove or disprove: If a and b are odd integers, then 4 | (a – b) or 4 | (a+b). -

A:

Q: Give a proof by contraposition of the following statement. If x is an integer and square of x is…

A: To do this, we must first state the contrapositive of what we set out to prove. so If x2 is even…

Q: Prove or disprove: There exist odd integers a and b such that 4 | (3a² + b²).

A: In this problem we have to prove or disprove: There exist odd integers  and  such that

Q: Prove that the absolute value of the product of two integers is equal to the product of the absolute…

A: Prove that the absolute value of the product of two integers is equal to the product of theabsolute…

Q: For all integers a, b and c, if a divides b and a divides c, then a divides (4b - 3c). True False

A: Answer is TRUE

Statements and Logic

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