Lesson 39 : Truth Values of Propositions

Slide 1

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Truth Values of Propositions

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Truth Values of Propositions

1 / 10

What is the truth value of the conditional [𝑝 ∧ (𝑞 ∨ 𝑟)] → [(𝑝 ∧ 𝑞) ∨ (𝑝 ∧ 𝑟)] if p and r are both true propositions and q is a false proposition?

a. true

b. false

c. neither true nor false

d. information is insufficient

2 / 10

What is the truth value of the conjunction ~𝑝 ∧ (𝑞 ∨ 𝑟) if p and q are both true
propositions and r is a false proposition?

a. true

b. false

c. neither true nor false

d. information is insufficient

3 / 10

In the minutes of the meeting, it is recorded that “All ten members agreed that there will be a monthly contribution of ₱50.00. Let p be the statement “The collection for February is ₱500.00”. Decide on the truth value of the negation ~p given the following scenarios. Scenario C: One member left the group. Which explains the reason behind the truth value of ~p given Scenario C?

Leaving the group does not relate to the total amount collected.

Scenario C does not mention whether the member contributed or not before leaving the group.

The remaining nine members divided ₱500.00 equally among themselves to meet the target amount.

With one member withdrawing his/her connection to the group, the collection shall be lower than ₱500.00.

4 / 10

In the minutes of the meeting, it is recorded that “All ten members agreed that there will be a monthly contribution of ₱50.00. Let p be the statement “The collection for February is ₱500.00”. Decide on the truth value of the negation ~p given the following scenarios. Scenario C: One member left the group. What is the truth value of the negation ~p given Scenario C?

a. true

b. false

c. neither true nor false

d. information is insufficient

5 / 10

In the minutes of the meeting, it is recorded that “All ten members agreed that there will be a monthly contribution of ₱50.00. Let p be the statement “The collection for February is ₱500.00”. Decide on the truth value of the negation ~p given the following scenarios. Scenario B: The treasurer lost the payment of the three members. Which explains the reason behind the truth value of ~p given Scenario B?

a. Scenario B lacks information.

b. Since three payments were lost, the total collection for February is ₱350.00 only.

c. The other seven members may or may not have paid more than ₱50.00 each.

d. Three payments were lost, but it is a thumbs rule that the one keeping the collection should make up the lost money.

6 / 10

In the minutes of the meeting, it is recorded that “All ten members agreed that there will be a monthly contribution of ₱50.00. Let p be the statement “The collection for February is ₱500.00”. Decide on the truth value of the negation ~p given the following scenarios. Scenario B: The treasurer lost the payment of the three members. Which explains the reason behind the truth value of ~p given Scenario B?

a. Scenario B lacks information.

b. Since three payments were lost, the total collection for February is ₱350.00 only.

c. The other seven members may or may not have paid more than ₱50.00 each.

d. Three payments were lost, but it is a thumbs rule that the one keeping the collection should make up the lost money.

7 / 10

In the minutes of the meeting, it is recorded that “All ten members agreed that there will be a monthly contribution of ₱50.00. Let p be the statement “The collection for February is ₱500.00”. Decide on the truth value of the negation ~p given the following scenarios. Scenario B: The treasurer lost the payment of the three members. Which explains the reason behind the truth value of ~p given Scenario B?

a. Scenario B lacks information.

b. Since three payments were lost, the total collection for February is ₱350.00 only.

c. The other seven members may or may not have paid more than ₱50.00 each.

d. Three payments were lost, but it is a thumbs rule that the one keeping the collection should make up the lost money.

8 / 10

In the minutes of the meeting, it is recorded that “All ten members agreed that there will be a monthly contribution of ₱50.00. Let p be the statement “The collection for February is ₱500.00”. Decide on the truth value of the negation ~p given the following scenarios. Scenario B: The treasurer lost the payment of the three members.What is the truth value of the negation ~p given Scenario B?

a. true

b. false

c. neither true nor false

d. information is insufficient

9 / 10

In the minutes of the meeting, it is recorded that “All ten members agreed that there will be a monthly contribution of ₱50.00. Let p be the statement “The collection for February is ₱500.00”. Decide on the truth value of the negation ~p given the following scenarios. Scenario A: All members of the group paid the monthly contribution.Which explains the reason behind the truth value of ~p given Scenario A?

a. Despite all members contributed, each may have contributed any amount.

b. Scenario A makes no mention about the contribution of each of ten members.

c. Given that all ten members of the group contributed, the total collection for February is ₱500.00.

d. Given that there are ten members of the group, the total collection for February just like in any month should be ₱500.00.

10 / 10

In the minutes of the meeting, it is recorded that “All ten members agreed that there will be a monthly contribution of ₱50.00. Let p be the statement “The collection for February is ₱500.00”. Decide on the truth value of the negation ~p given the following scenarios. Scenario A: All members of the group paid the monthly contribution. What is the truth value of the negation ~p given Scenario A?

a. true

b. false

c. neither true nor false

d. information is insufficient

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