Conditional
In the statement "If a figure is a square, then it has four sides," what is the hypothesis?
A figure is a square.
What is the converse of "If it rains, then the ground is wet"?
If the ground is wet, then it rains.
Which statement is logically equivalent to a conditional?
(Contrapositive)
What does p → q mean?
(Conditional Statement)
Reasoning from a general rule to a specific conclusion is called?
(Deductive Reasoning)
In the same statement, what is the conclusion?
(It has four sides.)
What is the inverse of "If a number is even, then it is divisible by 2"?
(If a number is not even, then it is not divisible by 2.)
Which pair of statements are logically equivalent?
(Converse and Inverse)
What does p ↔ q mean?
(Biconditional Statement)
Forming a general conclusion from patterns is called?
(Inductive Reasoning)
Identify the hypothesis: "If an angle measures 90°, then it is a right angle."
(An angle measures 90°.)
Write the contrapositive: "If a shape is a rectangle, then it has four sides."
(If a shape does not have four sides, then it is not a rectangle.)
A biconditional is formed by combining what two statements?
(Conditional and Converse)
What does p ∧ q mean?
(AND)
If "If a number is divisible by 5, then it ends in 0 or 5." The number is 45. What can you conclude?
(It ends in 0 or 5.)
Rewrite: "A polygon is regular only if all sides are equal" into an if-then statement.
(If a polygon is regular, then all its sides are equal.)
Write the biconditional: "If a figure is a square, then it has four equal sides."
(A figure is a square if and only if it has four equal sides.)
True or False: The inverse is logically equivalent to the conditional.
(False)
What does p ∨ q mean?
(OR)
"If a student studies, then the student passes." John studied. What is the conclusion?
(John passes.)
Identify both the hypothesis and conclusion: "If two angles are complementary, then their sum is 90°."
(Hypothesis: Two angles are complementary. Conclusion: Their sum is 90°.)
Given "If p, then q," write the converse, inverse, contrapositive, and biconditional.
(Converse: If q, then p; Inverse: If not p, then not q; Contrapositive: If not q, then not p; Biconditional: p if and only if q.)
Which statements are logically equivalent to each other?
(Conditional ↔ Contrapositive; Converse ↔ Inverse)
Match the symbols: →, ↔, ∧, ∨.
(→ Conditional; ↔ Biconditional; ∧ AND; ∨ OR)
"If a number is divisible by 10, then it is even." The number is not even. What conclusion can be made using the contrapositive?
(The number is not divisible by 10.)