Select the correct answer from each drop-down menu. how are evidence and counter examples used in proofs?

in a direct proof, evidence is used to __. on the other hand, a counter example is a single example that __.

1) support each statement
1a) contradict the last statement
1b) contradict the given information
1c) support the last statement

2)proves a proposition
2a) disproves given information
2b) proves the given information
2c) disproves a proposition

PLEASE HELP.

Geometry. i need step by step explanation on how to do each problem.

At a lunchron, guests are offered a selection of five different grilled vegetables and four different meats. in how many waya could one choose three vegetables and two meats?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?