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Build a truth table for the statement ~(pvq)^~p

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To build a truth table for the given statement ~(pvq)^~p, we need to consider all possible combinations of truth values for p and q.

Step 1: Determine the components of the statement

The given statement consists of three components: ~(pvq), ~p, and the overall statement.

Step 2: List all possible combinations of truth values for p and q

Since there are two variables, p and q, there are 2^2 = 4 possible combinations of truth values.

| p | q |

|---|---|

| T | T |

| T | F |

| F | T |

| F | F |

Step 3: Evaluate the components

~(pvq): This component is the negation of the disjunction (pvq). To evaluate this, we consider the disjunction (pvq) and then take the negation of the result.

| p | q | pvq | ~(pvq) |

|---|---|-----|--------|

| T | T | T | F |

| T | F | T | F |

| F | T | T | F |

| F | F | F | T |

~p: This component is the negation of p.

| p | ~p |

|---|----|

| T | F |

| F | T |

Step 4: Calculate the overall statement

The overall statement is the conjunction of ~(pvq) and ~p.

| p | q | pvq | ~(pvq) | ~p | (pvq)^~p |

|---|---|-----|--------|----|----------|

| T | T | T | F | F | F |

| T | F | T | F | F | F |

| F | T | T | F | T | F |

| F | F | F | T | T | T |

Step 5: Write the truth table

Finally, we can compile all the information into a truth table for the given statement ~(pvq)^~p.

| p | q | pvq | ~(pvq) | ~p | (pvq)^~p |

|---|---|-----|--------|----|----------|

| T | T | T | F | F | F |

| T | F | T | F | F | F |

| F | T | T | F | T | F |

| F | F | F | T | T | T |

Answer: The truth table for the statement ~(pvq)^~p is as shown above.

Step 1: Determine the components of the statement

The given statement consists of three components: ~(pvq), ~p, and the overall statement.

Step 2: List all possible combinations of truth values for p and q

Since there are two variables, p and q, there are 2^2 = 4 possible combinations of truth values.

| p | q |

|---|---|

| T | T |

| T | F |

| F | T |

| F | F |

Step 3: Evaluate the components

~(pvq): This component is the negation of the disjunction (pvq). To evaluate this, we consider the disjunction (pvq) and then take the negation of the result.

| p | q | pvq | ~(pvq) |

|---|---|-----|--------|

| T | T | T | F |

| T | F | T | F |

| F | T | T | F |

| F | F | F | T |

~p: This component is the negation of p.

| p | ~p |

|---|----|

| T | F |

| F | T |

Step 4: Calculate the overall statement

The overall statement is the conjunction of ~(pvq) and ~p.

| p | q | pvq | ~(pvq) | ~p | (pvq)^~p |

|---|---|-----|--------|----|----------|

| T | T | T | F | F | F |

| T | F | T | F | F | F |

| F | T | T | F | T | F |

| F | F | F | T | T | T |

Step 5: Write the truth table

Finally, we can compile all the information into a truth table for the given statement ~(pvq)^~p.

| p | q | pvq | ~(pvq) | ~p | (pvq)^~p |

|---|---|-----|--------|----|----------|

| T | T | T | F | F | F |

| T | F | T | F | F | F |

| F | T | T | F | T | F |

| F | F | F | T | T | T |

Answer: The truth table for the statement ~(pvq)^~p is as shown above.

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