Chapter 1.1-2:Universal and Existential Statements

What is a universal statement?

• A universal statement is a statement that applies to all members of a particular set or group.

• A universal statement is a statement that applies to no members of a particular set or group.

• A universal statement is a statement that applies to only one member of a particular set or group.

• A universal statement is a statement that applies to some members of a particular set or group.

Give an example of a universal statement.

• All mammals are warm-blooded.

• All fish live in water.

• All reptiles are cold-blooded.

• All birds are warm-blooded.

What is an existential statement?

• A statement that asserts the existence of at least one thing that satisfies a certain condition or property.

• A statement that asserts the non-existence of anything that satisfies a certain condition or property.

• A statement that asserts the existence of multiple things that satisfy a certain condition or property.

• A statement that denies the existence of anything that satisfies a certain condition or property.

Provide an example of an existential statement.

• There is a red car in the parking lot.

• There are no books on the shelf.

• There is a tree in the backyard.

• There exists a black cat in the room.

What is a universal conditional?

• A universal conditional is a logical statement that is true for all possible values of its variables.

• A universal conditional is a logical statement that is true for some possible values of its variables.

• A universal conditional is a logical statement that is false for all possible values of its variables.

• A universal conditional is a logical statement that is false for some possible values of its variables.

Give an example of a universal conditional statement.

• If all mammals have hair, then a dog has hair.

• If all birds can fly, then a penguin can fly.

• If all plants need sunlight, then a cactus needs sunlight.

• If all cars have wheels, then a bicycle has wheels.

What is the negation of a universal statement?

• Existential statement

• Disjunctive statement

• Conditional statement

• Contradictory statement

How can you prove a universal statement to be false?

• By using deductive reasoning

• By conducting an experiment

• By finding a counterexample

• By conducting a survey

What is the difference between a universal statement and an existential statement?

• A universal statement asserts that a property or condition is true for all elements, while an existential statement asserts that a property or condition is true for some elements.

• The difference between a universal statement and an existential statement is that a universal statement asserts that a property or condition is true for every element, while an existential statement asserts that there exists at least one element with a certain property.

• A universal statement asserts that a property or condition is true for no elements, while an existential statement asserts that a property or condition is true for at least one element.

• A universal statement asserts that a property or condition is true for some elements, while an existential statement asserts that a property or condition is true for all elements.

Explain the concept of existential import in universal statements.

• Existential import refers to the assumption of existence in universal statements.

• Existential import refers to the negation of existence in universal statements.

• Existential import refers to the exclusion of existence in universal statements.

• Existential import refers to the implication of existence in universal statements.