Descreat Math Problom 4) c and f Prove or disprove each of these propositions. (

Question

Descreat Math Problom 4) c and f

Prove or disprove each of these propositions. (a) If p and q are prime numbers, then pq+ 1 is a prime number. (b) If x and y are positive integers with x > y + 1, then x^2 - y^2 is not prime. (c) If Tom has at most n brothers and Chris is Tom's sibling, then Chris has at most n brothers. (d) If a and b are positive integers, then Squareroot a^2 + b^2 - a + b. (e) Every even number can be written as the sum of an odd number and a perfect square. (f) The product of a multiple of 6 and a multiple of 10 is a multiple of 60.

Explanation / Answer

c) false

let tom have b brothers and s sisters. we know b<=n
if chris is a brother, he will share the remaining b-1 brothers with tom, and will have tom as a brother as well. i.e. he'll have b brothers.
now if chris is a sister: chris will share tom's b brothers, as well as tom, i.e. chris will have b+1 brothers.
if b<=n, then b+1<=n+1, hence chris can have more than n brothers if she is a girl

f ) let a multiple of 6 be 6x, multiple of 10 be 10y
then the product is 6x * 10y=60xy, which is a multiple of 60

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