Let If p: prasad work hard.
q: prasad gets good grade.
The verbal from for `(~p rarr q)` is

Options

A. If prasad word hard then he get good grade
B. If prasad does not work hard then he gets good grade.
C. If prasad does not work hard then he does not gets good grade
D. If prasad work hard then he does not gets good grade.

Answer

To solve the problem, we need to express the negation of the implication \( \neg p \rightarrow q \) in verbal form. Let's break this down step by step.

### Step 1: Understand the Variables
- Let \( p \) represent "Prasad works hard."
- Let \( q \) represent "Prasad gets good grades."

### Step 2: Identify the Implication
The implication \( p \rightarrow q \) can be read as "If Prasad works hard, then he gets good grades."

### Step 3: Write the Negation
We need to find the verbal form of the negation of the implication \( \neg p \rightarrow q \). The negation of \( p \) is represented as \( \neg p \), which means "Prasad does not work hard."

### Step 4: Formulate the Negation
The expression \( \neg p \rightarrow q \) translates to "If Prasad does not work hard, then he gets good grades."

### Step 5: Final Verbal Form
Thus, the verbal form of \( \neg p \rightarrow q \) is:
"If Prasad does not work hard, then he gets good grades."

### Summary
The verbal form of the statement \( \neg p \rightarrow q \) is:
"If Prasad does not work hard, then he gets good grades."

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