Find the smallest distinct postive numbers that provide a counterexample to show the statement is false.  The sum of any two different odd numbers plus any even number is odd.  The counterexample is   _+_+_=

Q: are there any even numbers greater than 2 which are prime? why or why not?

A: We will find the solution in the following step

Q: Prove that the last two digits of 2" cannot be 02 and the last three digits cannot be 108.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Rationalize the denomi 20 5/10 - 7/5

A: 20510-75

Q: 6) find all the and non residues (mods) incongruent quadratic residues

A: It is given that Incongurant quadratic residues.

Q: Find the number of positive integers X smaller than 12849 which have exactly 2022 positive divisors

A: Theory : Total no of divisor of a number, If its prime factorization, given by ∏i=1hpiai Where p is…

Q: A witness on a hit and run incident cannot recall the whole plate number of the car who hit an old…

A: Given that in hit and run case an old woman remembered is the plate number starts with TIP and the…

Q: Consider all positive integers that are mueiples of 20 and that are less than or equal to 300. What…

A:

Q: Find a counterexample to the statement. The product of any integer and itself is even. Answer How to…

A: Given:         The product of any integer and itself is even.   Let us take an integer =2 When we…

Q: Show that every positive integer can be written as the product of a square (possibly 1) and a…

A:

Q: Select all the expressions that are greater than 3. Be sure to show your work 1.67 + 1.4 2.97 +…

A: We have to select all the expressions that are greater than 3. (1) 1.67 + 1.4  = 3.07 > 3

Q: An identity thief is trying to break into someone's computer that is protected by a 4-digit passcode…

A:

Q: Which term of the expansion of (x° + 7) contains x 28 ,36 Term number contains æ36

A:

Q: Prove that the sum of any five consecutive positive integers is always a multiple of five.

A:

Q: The sum of all positive integers less than 300 which are divisible by 3.

A:

Q: Prove that an odd number multiplied by an odd number is odd.

A: The objective is to prove that an odd number multiplied by an odd number is odd.

Q: witness to a hit-and-run accident told the police that the license number contained the letters RQLH…

A: Answer:72 Explanation: First digit=2 No.of digits=10 ie, (0,1,2,3,4,5,6,7,8,9) Now possibilities…

Q: Find: The sum of all positive integers less than 400 which are not divisible by 5.

A:

Q: How to find the last two ditgits of 2^2021 ?

A: Solve the given problem.

Q: Determine the smallest integer that can be expressed as a sum of two primes in three different ways

A: Let us have smallest prime numbers  are, 2,3,5,7,11,13 17,19.....

Q: Find the number of strings of length 8 of lower case letters of the alphabet, with repeated letters…

A: The length of the string is 8 and one letter are given , begin with v or end with f. We have to…

Q: What two nonnegative real numbers with a sum of 34 have the largest possible product?

A:

Q: "Every positive integer can be written as the sum of the square of 3 positive integers." prove…

A: Given: "Every positive integer can be written as the sum of the square of 3 positive integers." To…

Q: The 4th term of an ap is zero. Prove that 25th term of the AP is three times its 11th term

A:

Q: Show that, selecting 91 positive integers guarantees that there are at least 10 integers with the…

A:

Q: The sum of all positive integers less than 300 which are not divisible by 3.

A: Sum of n positive integer is given by, Sn=nn+12

Q: what two consective odd integers have a product of 63?

A: Find two odd integers.

Q: 5. Give a recursive definition of the set of positive integers that are multiples of 5.

A: Solution

Q: Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3 when it…

A: (a)The fill up for the statement to rewrite the given statement: Is there an integer n such that n…

Q: If two integers have the same parity, then their sum is even. (Try cases.)

A: According to the given information it is required to prove that the sum of two integers of same…

Q: Prove: “The sum of two even integers is even.”

A: To prove: The sum of two even integers is even. n is an even number if it can be expressed as n =…

Q: If the sum of two counting numbers is an even number, then the product of the two counting numbers…

A: ANSWER:- 1) From the given statement, If the sum of two counting numbers is an even counting number,…

Q: Which numbers in Z17 are relatively prime to 17? Enter your answer as a comma separated list of…

A: The objective of the question is determine all al relatively prime to 17 in Z17 .

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT, Apply the principle of inclusion-exclusion Determines the…

A: The principle of inclusion-exclusion Let A and B are two set then the union of A and B has number of…

Q: provide a recursive definition for the set Y of all negative multiples of 7.

A: Consider the provided question, Recursive definition: Recursion is the general definition term for…

Q: find all three-digit number with different digits with the property that those numbers are divisible…

A:

Q: If x is an odd integer then 5x – 7 is an even integer. (use direct proof)

A: Given that “x” is an odd integer then “5x-7” is an even integer.

Q: Choose two distinct integers, x and y, between 0 and 9. Derive the number of 9- digit integers that…

A:

Q: Prove that no number of form 4k+3 (where K is a positive integer) can ever be the sum of two perfect…

A:

Q: is there integer that has reminder of 2 when its devided by 5?

A: There are infinite number of integers that has reminder of 2 when its divided by 5

Q: What is the smallest sum possible sum of 25 consecutive positive integers which s a perfect square?

A: Let's take the 25 consecutive positive numbers as an Arithmetic Progression with first term a.…

Q: 4. ( it as linear combination of both numbers. Find the greatest common divisor of the numbers 1520…

A:

Q: Determine the smallest integer that can be expressed as a sum of two primes in three different ways.

A: The number is 22 and all others smallest integer can not be written as sum of two primes in three…

Q: Prove by contradiction that 2020 cannot be written as a sum of 3 odd integers.

A: The objective is to prove  that 2020 cannot be written as a sum of 3 odd integers by the…

Q: 5!, called 5_______ , is the product of all positive integers from_________ down through________ .…

A: For any positive integer n, n! is the product of all the positive integers  from 1 to n. That is,…

Q: Put a positive whole number in each of the four boxes of this table that satisfies the rule. For…

A: Prime number is a positive integer having exactly 2 factors. for example 7 is a odd prime number as…

Q: The chairs of an auditorium are to be labeled with a letter and a positive integer not exceeding…

A: Given: The chairs of an auditorium are to be labeled with a letter and a positive integer not…

Q: Suppose that n students take a quiz and their scores sum to 150. What is the smallest number n to…

A: Pigeonhole Principle: The pigeonhole principle states that if n items are put into m containers with…

Q: Suppose that all the pages are black and white, but each group of 25 consecutivepages (1-25, 26-50,…

A: To determine the number of ways for the 125 pages to assign to the 5 printers. Given that, the total…

Statements and Logic

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