Test — Test Answers

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If an original conditional statement is represented using p → q, which represents the converse?

Given:p: Angles XYZ and RST are vertical angles.q: Angles XYZ and RST are congruent.Which statement is logically equivalent to p → q?

Let p: The shape is a rhombus.Let q: The diagonals are perpendicular.Let r: The sides are congruent.Which represents "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent”?

Let p: A student plays basketball.Let q: A student plays tennis.

What is the inverse of the conditional statement?If a polygon has five angles, then it is a pentagon.

The truth table represents statements p, q, and r. pqrq ∧ r ATT T T BTTF F C T FT F DT F FF EF T T T FF T F F GF F T F HF F F F

A flowchart proof

Read the statement.Doubling the dimensions of a rectangle increases the area by a factor of 4.If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4, which are true? Select two options.p → q represents the original conditional statement.~p → ~q represents the inverse of the original conditional statement.q → p represents the original conditional statement.~q → ~p represents the converse of the original conditional statement.p → ~q represents the contrapositive of the original conditional statement.

Let p: The number is even.Let q: The number is prime.Which statement is represented by p ∧ q?

What is the missing reason in the proof?Given: ∠ABC is a right angle, ∠DBC is a straight angleProve: ∠ABC ≅ ∠ABD

The diagram represents responses to a survey that include statements p and q.

Which pairs of statements are logically equivalent? Select two options.the inverse and the contrapositive of the original conditional statementthe original conditional statement and its contrapositivethe original conditional statement and its inversethe converse and the inverse of the original conditional statementthe converse and the contrapositive of the original conditional statement

Which disjunction is always true for any real number x?

If p is the hypothesis of a conditional statement and q is the conclusion, which is represented by ~p → ~q?

Given:p: 2x = 16q: 3x – 4 = 20Which is the converse of p → q?

A paragraph proof

4 lines extend from point B. A line extends straight up from B to point A. Another line extends up and to the right to point C. Another line extends slight up and to the right to point D. The other line extends slightly down and to the right to point E.

Let p: x 3What is represented by p ∨ q?