KN U2 D9 Logic and Statements Quiz

Indicate whether the statement "If the electricity goes out then the standard telephone will still work" is a simple statement or a compound statement.

• Simple statement

• Compound statement (Conjunction)

• Compound statement (Disjunction)

• Compound statement (Conditional)

Answer explanation

The statement "If the electricity goes out then the standard telephone will still work" is a conditional statement, as it expresses a cause-and-effect relationship. Therefore, it is classified as a compound statement (Conditional).

Indicate whether the statement "If Cathy Smith walks 4 miles today then she will be sore tomorrow" is a simple statement or a compound statement.

• Simple statement

• Compound statement (Conjunction)

• Compound statement (Disjunction)

• Compound statement (Conditional)

Answer explanation

The statement "If Cathy Smith walks 4 miles today then she will be sore tomorrow" is a conditional statement, as it expresses a cause-and-effect relationship between walking and being sore.

Write the statement "The bonfire is not burning if and only if the tent is not pitched" in symbolic form if p: The tent is pitched and q: The bonfire is burning.

• p ↔ q

• ~p ↔ q

• p ↔ ~q

• ~p ↔ ~q

Answer explanation

The statement "The bonfire is not burning if and only if the tent is not pitched" translates to ~q ↔ ~p. Reversing the order gives ~p ↔ ~q, which is the correct symbolic form. Thus, the answer is ~p ↔ ~q.

Write the statement in symbolic form if: p: The charcoal is hot. q: The chicken is on the grill. The charcoal is not hot, but the chicken is on the grill.

• ~p ∧ q

• p ∧ ~q

• ~p ∨ q

• p ∨ ~q

Answer explanation

The statement "The charcoal is not hot, but the chicken is on the grill" translates to ~p (not hot) and q (on the grill). In symbolic form, this is represented as ~p ∧ q, which is the correct choice.

Write the statement in symbolic form if: p: The charcoal is hot. q: The chicken is on the grill. It is false that the charcoal is hot and the chicken is on the grill.

• ~(p ∧ q)

• ~p ∧ ~q

• ~(p ∨ q)

• p ∧ ~q

Answer explanation

The statement "It is false that the charcoal is hot and the chicken is on the grill" translates to the negation of the conjunction of p and q, which is represented as ~(p ∧ q). Thus, the correct choice is ~(p ∧ q).

Write the statement in symbolic form if: p: The temperature is 90°F. q: The air conditioner is working. r: The apartment is hot. If the apartment is hot and the air conditioner is working, then the temperature is 90°F.

• (r ∧ q) → p

• (r ∧ q) → ~p

• (r ∨ q) → p

• (r ∨ q) → ~p

Answer explanation

The statement "If the apartment is hot and the air conditioner is working, then the temperature is 90°F" translates to (r ∧ q) → p, where r is 'the apartment is hot', q is 'the air conditioner is working', and p is 'the temperature is 90°F'.

If the car has the gas and the battery is charged then the car will start.

• Conditional

• Conjunction

• Disjunction

• Biconditional

Answer explanation

The statement describes a situation where the car will start if two conditions are met: having gas and a charged battery. This is a classic example of a conditional statement, where one event depends on the occurrence of another.

Determine the truth value for the statement: 3 + 5 = 4 + 4 or 10 - 9 = 9 - 10

• True

• False

• Neither

• Cannot be determined

Answer explanation

The statement is true because 3 + 5 equals 8, which is the same as 4 + 4, and 10 - 9 equals 1, which is not the same as 9 - 10 (-1). However, since the first part is true, the entire statement is true due to the 'or' operator.

Write the statement in symbolic form if: p: The light is on. q: The door is open. The light is on or the door is not open.

• p ∨ ~q

• ~p ∨ q

• p ∧ ~q

• ~p ∧ q

Answer explanation

The statement "The light is on or the door is not open" translates to p ∨ ~q. Here, p represents "The light is on" and ~q represents "The door is not open," making p ∨ ~q the correct symbolic form.

Determine the truth value for the statement: 7 - 2 = 5 or 8 + 1 = 10

• True

• False

• Neither

• Cannot be determined