In each of the following questions, we ask you to prove a statement. List all the steps in each proof, ang give the reason for each step.
1 . Prove that the sum of two consecutive odd numbers is divisible by 4.

In each of the following questions, we ask you to prove a statement. List all the steps in each proof, ang give the reason for each step. 4. Let x and y be rational numbers. Show that xy is a rational number.

In each of the following questions, we ask you to prove a statement. List all the steps in each proof, ang give the reason for each step. 5. If a and b positive integers, then you know that a =bq +r, 0 £ r lt b , where q is a whole number. Prove that HCF (a,b) =HCF (b,r).

In each of the following questions, we ask you to prove a statement. List all the steps in each proof, ang give the reason for each step. 6. A line parallel to side BC of a triangle ABC ,intersects AB and AC at D and E respectively. Prove that (AD)/(DB)=(AE)/(EC) .

In each of the following questions, there are two statements. State if the second is the negation of the first or not. (iii) All elephants are huge. One elephant is not huge.

In each of the following questions, there are two statements. State if the second is the negation of the first or not. (iv) All fire engines are red. All fire engines are not red.

Find the values of the letters in each of the following and give reasons for the steps involved A 1 +1 B=B 0

Find the values of the letters in each of the following and give reasons for the steps involved 1 A xx A=9 A

Find the values of the letters in each of the following and give reasons for the steps involved A B +3 7=6 A

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. If x ∈ A and A ∈ B , then x ∈ B

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. If A ⊂ B and B ∈ C , then A ∈ C