The following question consist of two statements, one labelled as the 'Assertion (A)' and the other as 'Reason (R)' You are to examine these two statements carefully and select the answer.
Assertion (A) : If `P(A) = 3/4 and P(B) = 3/8,` then
`P(A uu B) ge 3/4`
Reason (R) : `P(A) le P(A uu B) and P(B) le P(A uu B)`, hence
`P(A uu B) ge " max ". {P(A), P(B)}`

Options

A. Both A and R are individually true, and R is the correct explanation of A.
B. Both A and R are individually true but R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.

Explanation

To solve the given problem, we need to analyze the two statements: the Assertion (A) and the Reason (R).

### Step 1: Understand the Assertion (A)
The assertion states:
- \( P(A) = \frac{3}{4} \) and \( P(B) = \frac{3}{8} \)
- It claims that \( P(A \cup B) \geq \frac{3}{4} \)

### Step 2: Understand the Reason (R)
The reason states:
- \( P(A) \leq P(A \cup B) \) and \( P(B) \leq P(A \cup B) \)
- It concludes that \( P(A \cup B) \geq \max\{P(A), P(B)\} \)

### Step 3: Analyze the Maximum Probability
From the values given:
- \( P(A) = \frac{3}{4} \)
- \( P(B) = \frac{3}{8} \)

Now, we calculate \( \max\{P(A), P(B)\} \):
- \( \max\left\{\frac{3}{4}, \frac{3}{8}\right\} = \frac{3}{4} \)

### Step 4: Use the Properties of Probability
According to the properties of probability:
- \( P(A \cup B) \geq \max\{P(A), P(B)\} \)
- Therefore, \( P(A \cup B) \geq \frac{3}{4} \) is indeed true.

### Step 5: Conclusion on Assertion and Reason
- The assertion \( P(A \cup B) \geq \frac{3}{4} \) is true.
- The reason \( P(A) \leq P(A \cup B) \) and \( P(B) \leq P(A \cup B) \) leading to \( P(A \cup B) \geq \max\{P(A), P(B)\} \) is also true.

### Step 6: Evaluate the Explanation
However, while both statements are true, the reason does not provide a direct explanation for the assertion. The assertion stands on its own based on the properties of probabilities.

### Final Answer
Both Assertion (A) and Reason (R) are true, but the Reason (R) is not the correct explanation for Assertion (A).