Logical Statements and Connectives

This video tutorial introduces mathematical statements and logic connectives. It explains the difference between atomic and molecular statements, provides examples of each, and discusses how to classify statements. The tutorial also covers logical connectives, including conjunctions, disjunctions, implications, biconditionals, and negations, with examples to illustrate their use.

What is an atomic statement?

• A statement that can be divided into smaller statements

• A statement that is always false

• A statement that cannot be divided into smaller statements

• A statement that is always true

Which of the following is NOT a statement?

• Telephone numbers in the U.S. have 10 digits

• 42 is a perfect square

• Would you like some cake?

• The moon is made of cheese

Why is '3 plus x equals 12' not considered a statement?

• Because it is always true

• Because it is a question

• Because it lacks a specific value for x

• Because it is a command

What type of statement is 'You order a pizza and you order a drink'?

• Not a statement

• Atomic statement

• Conditional statement

• Molecular statement

Which logical connective is used in the statement 'If p then q'?

• Negation

• Implication

• Disjunction

• Conjunction

What is a binary connective?

• A connective that is always false

• A connective that is always true

• A connective that connects two statements

• A connective that applies to a single statement

Which of the following is a unary connective?

• Or

• And

• If and only if

• Not

What type of statement is 'The cardinals will win the super bowl or I'll lose $100'?

• Not a statement

• Molecular statement

• Conditional statement

• Atomic statement

What is the logical connective in the statement 'The number 15 is odd and composite'?

• Or

• If

• Not

• And

Which statement is an example of a negation?

• Every even number is divisible by 2

• It is not the case that all rectangles are squares

• You can't win if you don't try

• The cardinals will win the super bowl