Contra - positive of
p: "If x and y are integers such that xy is odd then both x and y are odd" is

Options

A. If both x and y are odd, then xy is odd
B. If both x and y are even, then xy is even
C. If x or y is odd, then xy is odd
D. If either x or y is not odd then product xy is not odd

Answer

To find the contrapositive of the statement "If x and y are integers such that xy is odd, then both x and y are odd," we will follow these steps:

### Step 1: Identify the original statement
The original statement can be expressed in the form of a conditional statement:
- **P**: "xy is odd"
- **Q**: "Both x and y are odd"

So, the original statement can be written as:
- If P, then Q (P → Q)

### Step 2: Write the negation of Q
To find the contrapositive, we need to negate Q:
- Negation of Q: "At least one of x or y is not odd" (which means at least one is even).

### Step 3: Write the negation of P
Next, we also need to negate P:
- Negation of P: "xy is not odd" (which means xy is even).

### Step 4: Formulate the contrapositive
The contrapositive of the statement "If P, then Q" is "If not Q, then not P." Therefore, we can write:
- If at least one of x or y is not odd (not Q), then xy is not odd (not P).

### Final Contrapositive Statement
Thus, the contrapositive of the original statement is:
- "If at least one of x or y is not odd, then xy is even."