Let a,b,c and d represent simple statements. Assume that `a ^^ d` is true, `b ^^ c` is false, and ~c is false.
What is the truth value of a ?

Answer

To determine the truth value of \( a \) given the statements, we can follow these steps:

1. **Identify the given statements:**
- \( a \land d \) is true.
- \( b \land c \) is false.
- \( \neg c \) is false.

2. **Analyze the statement \( \neg c \) is false:**
- If \( \neg c \) is false, then \( c \) must be true.
- Therefore, we have:
\[ c = \text{true} \]

3. **Analyze the statement \( b \land c \) is false:**
- The conjunction \( b \land c \) is false. For a conjunction to be false, at least one of the statements must be false.
- Since \( c \) is true (from step 2), \( b \) must be false.
- Therefore, we have:
\[ b = \text{false} \]

4. **Analyze the statement \( a \land d \) is true:**
- The conjunction \( a \land d \) is true. For a conjunction to be true, both statements must be true.
- Therefore, both \( a \) and \( d \) must be true.
- Thus, we conclude:
\[ a = \text{true} \]

5. **Final conclusion:**
- The truth value of \( a \) is true.

### Summary of Truth Values:
- \( a = \text{true} \)
- \( b = \text{false} \)
- \( c = \text{true} \)
- \( d = \text{true} \) (since \( a \land d \) is true)