Geometry SOL REVIEW TOPIC 1 (G.1) – Logic

Consider the following statement: If 4x = 8, then x = 2. Which is the Inverse of the statement?

• If x = 2, then 4x ≠ 8.

• If x ≠ 2, then 4x ≠ 8.

• If x = 2, then 4x = 8.

• If 4x ≠ 8, then x ≠ 2.

Using deductive reasoning, if the first two statements are true, then which third statement is invalid?

• A. p → q, q → ~v, ∴ ~v → ~p

• B. p → q, q → ~v, ∴ ~p → ~v

• C. p → q, q → v, ∴ p → v

• D. ~p → ~q, ~q → ~v, ∴ ~p → ~v

Conjecture: I see the classroom floor is covered in brown tile, therefore all of the floors in the school must be covered in brown tile. Which of the following could be counter examples?

• The gym floor is wooden boards.

• the hall is tiled in blue/gray tile.

• the main office floor is carpeted.

• The parking lot is black topped.

Tags

CCSS.RI.8.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.8.8

CCSS.RL.7.1

Write the symbolic notation for the following statement: Yams are not round if and only if rocks are round. (If p represents "yams are orange" and q represents "rocks are round")

• ¬q ↔ q

• p ↔ q

• ¬p ↔ q

• p ↔ ¬q

If it is alive, large, and gray, then it must be an elephant. Which would be a counterexample for the conjecture given?

• big gray rocks

• a pink elephant

• a rhinoceros

• a mouse

If you add two numbers you always get a larger value. Choose all that are counterexamples for the given conjecture.

• 2 - 3 = -1

• 3 + 3 = 6

• -2 + -2 = -4

• 0 + 0 = 0

Tags

CCSS.7.NS.A.1B

If there are clouds in the sky today, then it is going to rain. What is the contrapositive of the statement?

• If there are no clouds in the sky today, then it is not going to rain.

• If it is going to rain today, then there are clouds in the sky.

• If it is not going to rain today, then there are no clouds in the sky.

• If there are clouds in the sky today, then it is not going to rain.

What is the converse of the following statement? If Joe goes fishing, then he needs bait.

• If he does not need bait, then Joe does not go fishing.

• If he needs bait, then Joe goes fishing.

• If Joe does not go fishing, then he does not need bait.

• If Joe goes fishing, then he does not need bait.

Let p = You play basketball. Let q = You play a sport. Argument: If you do not play basketball, then you play a sport. Which of the following is the symbolic representation of the given argument?

• ~q → p

• ~p → ~q

• q → p

• ~p → q

Which is a valid conclusion that can be drawn from these statements? If a quadrilateral is a rhombus, then it is a parallelogram. If a quadrilateral is a parallelogram, then its opposite angles are congruent.

• Every quadrilateral is a rhombus.

• Every parallelogram is a rhombus.

• Opposite angles of a rhombus are congruent.

• Opposite angles of a quadrilateral are congruent.

Tags

CCSS.HSG.CO.C.11