Consider the following conditional statement: If Bill's car will start and he has enough gas, then he will pick up Brenda and they will go bowling. a) Write the contrapositive of the original statement (using propositional variables) b) Write the truth table for the original statement

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**Conditional Statement Exercise**

1. Consider the following conditional statement:

   *If Bill’s car will start and he has enough gas, then he will pick up Brenda and they will go bowling.*

   a) Write the contrapositive of the original statement (using propositional variables).

   b) Write the truth table for the original statement.

**Task:** Use Visio to draw a circuit that implements an Exclusive OR circuit, using only basic gates. Insert your drawing here.

---

**Explanation of Concepts:**

- **Conditional Statement:** A logical statement with a hypothesis followed by a conclusion. In this case, the condition is about Bill's car starting and having gas, and the result is picking up Brenda and going bowling.
  
- **Contrapositive:** The contrapositive of a conditional statement "If P, then Q" is "If not Q, then not P." It is logically equivalent to the original statement.

- **Truth Table:** A table used in logic to determine the truth value of a logical expression based on all possible combinations of its components.

- **Exclusive OR (XOR) Circuit:** A digital logic gate that outputs true or 1 only when the inputs to it are unequal. The XOR gate can be constructed using basic logic gates such as AND, OR, and NOT.
Transcribed Image Text:**Conditional Statement Exercise** 1. Consider the following conditional statement: *If Bill’s car will start and he has enough gas, then he will pick up Brenda and they will go bowling.* a) Write the contrapositive of the original statement (using propositional variables). b) Write the truth table for the original statement. **Task:** Use Visio to draw a circuit that implements an Exclusive OR circuit, using only basic gates. Insert your drawing here. --- **Explanation of Concepts:** - **Conditional Statement:** A logical statement with a hypothesis followed by a conclusion. In this case, the condition is about Bill's car starting and having gas, and the result is picking up Brenda and going bowling. - **Contrapositive:** The contrapositive of a conditional statement "If P, then Q" is "If not Q, then not P." It is logically equivalent to the original statement. - **Truth Table:** A table used in logic to determine the truth value of a logical expression based on all possible combinations of its components. - **Exclusive OR (XOR) Circuit:** A digital logic gate that outputs true or 1 only when the inputs to it are unequal. The XOR gate can be constructed using basic logic gates such as AND, OR, and NOT.
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