1. **Problem Statement:** We are given two whole numbers $c$ and $d$. We need to determine which of the following statements about the parity (odd or even) of $2c + 3d$ are true: - If $c$ is odd and $d$ is odd then $2c + 3d$ is odd - If $c$ is even and $d$ is odd then $2c + 3d$ is odd - If $c$ is odd and $d$ is even then $2c + 3d$ is odd - If $c$ is even and $d$ is even then $2c + 3d$ is odd 2. **Key Concepts:** - An even number multiplied by any integer remains even. - An odd number multiplied by an odd integer remains odd. - The sum of two even numbers is even. - The sum of two odd numbers is even. - The sum of an even and an odd number is odd. 3. **Analyze each case:** - Case 1: $c$ odd, $d$ odd - $2c$ is $2 \times$ odd = even - $3d$ is $3 \times$ odd = odd - Sum: even + odd = odd - Statement is **true**. - Case 2: $c$ even, $d$ odd - $2c$ is $2 \times$ even = even - $3d$ is $3 \times$ odd = odd - Sum: even + odd = odd - Statement is **true**. - Case 3: $c$ odd, $d$ even - $2c$ is $2 \times$ odd = even - $3d$ is $3 \times$ even = even - Sum: even + even = even - Statement is **false**. - Case 4: $c$ even, $d$ even - $2c$ is $2 \times$ even = even - $3d$ is $3 \times$ even = even - Sum: even + even = even - Statement is **false**. 4. **Final answers:** - True: If $c$ is odd and $d$ is odd - True: If $c$ is even and $d$ is odd - False: If $c$ is odd and $d$ is even - False: If $c$ is even and $d$ is even Thus, tick the boxes for the first two statements only.