What is logical reasoning used for in mathematics?

• To verify the correctness of programs

• To draw conclusions from experiments

• To prove theorems

• To solve a multitude of problems

What is a statement or proposition?

• A sentence that is always false

• A sentence that is either true or false

• A sentence that is neither true nor false

• A sentence that is always true

What does the negation of a proposition involve?

• Using the symbol ¬ at the end of the proposition

• Introducing the word 'not' at the end of the proposition

• Prefixing the phrase 'it is not the case that' in the proposition

• Adding the phrase 'It is false that' at the beginning of the proposition

When is the conjunction of two propositions true?

• When both propositions are true

• When neither proposition is true

• When at least one proposition is true

• When both propositions are false

What is the disjunction of two propositions?

• Both propositions are true

• At least one proposition is true

• Both propositions are false

• Neither proposition is true

When is a conditional statement false?

• When the hypothesis is false and the conclusion is true

• When both the hypothesis and conclusion are true

• When both the hypothesis and conclusion are false

• When the hypothesis is true and the conclusion is false

What is logical equivalence?

• The compound statement 'P and Q'

• The compound statement 'P or Q'

• The compound statement 'P if and only if Q'

• The compound statement 'P and not Q'

What do De Morgan's Laws state?

• The negation of an and statement is equivalent to the and statement

• The negation of an or statement is equivalent to the or statement

• The negation of an or statement is equivalent to the and statement

• The negation of an and statement is equivalent to the or statement

What is a tautology?

• A statement form that is always false

• A statement form that is sometimes true

• A statement form that is always true

• A statement form that is sometimes false

What is a contradiction or an absurdity?

• A statement form that is always true

• A statement form that is sometimes true

• A statement form that is sometimes false

• A statement form that is always false