Determine whether p,q and "If p, then q " are true or false in each case given below :p :
5<7, q : 5 is an odd number

Answer

To determine the truth values of the statements \( p \), \( q \), and the implication "If \( p \), then \( q \)", we will analyze each statement step by step.

### Step 1: Evaluate Statement \( p \)
The statement \( p \) is given as:
\[ p: 5 < 7 \]

**Truth Value of \( p \):**
- The statement \( 5 < 7 \) is true because 5 is indeed less than 7.

### Step 2: Evaluate Statement \( q \)
The statement \( q \) is given as:
\[ q: 5 \text{ is an odd number} \]

**Truth Value of \( q \):**
- The statement \( 5 \text{ is an odd number} \) is also true because 5 is not divisible by 2, which defines an odd number.

### Step 3: Evaluate the Implication "If \( p \), then \( q \)"
The implication is given as:
\[ \text{If } p, \text{ then } q \]

This can be written in logical notation as:
\[ p \implies q \]

**Truth Value of \( p \implies q \):**
- An implication \( p \implies q \) is true unless \( p \) is true and \( q \) is false.
- Since both \( p \) and \( q \) are true, the implication \( p \implies q \) is also true.

### Summary of Truth Values
- \( p \): True
- \( q \): True
- \( p \implies q \): True

### Final Conclusion
All statements \( p \), \( q \), and the implication \( p \implies q \) are true.

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