Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed. 5x6-4=21 implies 2 (`5 -: 15+3`)=`20/3`

Answer

To solve the problem, we need to evaluate the two statements given and determine their truth values. Then, we will analyze the conditional statement formed by these two statements.

**Step 1: Define the statements.**
Let:
- \( p \): \( 5 \times 6 - 4 = 21 \)
- \( q \): \( 2 \times \left( \frac{5}{15} + 3 \right) = \frac{20}{3} \)

**Step 2: Evaluate statement \( p \).**
Calculate \( 5 \times 6 - 4 \):
\[ 5 \times 6 = 30 \\ 30 - 4 = 26 \]
So, \( 5 \times 6 - 4 \) equals 26, not 21. Therefore, statement \( p \) is **false**.

**Step 3: Evaluate statement \( q \).**
Calculate \( 2 \times \left( \frac{5}{15} + 3 \right) \):
First, simplify \( \frac{5}{15} \):
\[ \frac{5}{15} = \frac{1}{3} \]
Now, add 3:
\[ \frac{1}{3} + 3 = \frac{1}{3} + \frac{9}{3} = \frac{10}{3} \]
Now multiply by 2:
\[ 2 \times \frac{10}{3} = \frac{20}{3} \]
So, statement \( q \) is **true**.

**Step 4: Determine the truth value of the conditional \( p \implies q \).**
In logic, a conditional statement \( p \implies q \) is false only when \( p \) is true and \( q \) is false. In all other cases, it is true. Here, we have:
- \( p \) is false (F)
- \( q \) is true (T)

Since \( p \) is false, the conditional \( p \implies q \) is **true**.

**Final Answer:**
- \( p \): F
- \( q \): T
- Truth value of \( p \implies q \): T

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