Logic Statements

(Basic)

Rewrite the conditional statement in if-then form.

When a glacier melts, the sea level rises

If ​ (a)   , then ​ (b)   .

• a glacier melts

• the sea level rises

• a glacier doesn't melt

• the sea level doesn't rise

Answer explanation

The question asks to rewrite the statement 'When a glacier melts, the sea level rises' in if-then form. The correct way to do this is 'If a glacier melts, then the sea level rises'. This is because the conditional statement 'If a glacier melts' is the cause, and 'the sea level rises' is the effect or result.

Tags

G.4B

(Intermediate)

Rewrite the conditional statement in if-then form.

Two right angles are supplementary angles.

If ​ (a)   , then ​ (b)   .

• two angles are right angles

• the angles are supplementary

• two angles are not supplementary

• the angles are not right angles

Answer explanation

The statement 'Two right angles are supplementary angles' means that if two angles are right angles, then they are supplementary. This is because a right angle measures 90 degrees and when two right angles are added together, it equals 180 degrees which is the definition of supplementary angles.

Tags

G.4B

• two angles are complementary

• the angles' measures sum to 90 degrees

• the angles' measures do not sum to 90 degrees

• two angles are not complementary

Answer explanation

The given question asks to rewrite the conditional statement about complementary angles. Complementary angles are two angles that add up to 90 degrees. So, the correct if-then form would be, 'If two angles are complementary, then the angles' measures sum to 90 degrees'.

Tags

G.4B

(Basic)

Write the negation of the statement.

p: The ball is not pink.

~p: ​ (a)  

• The ball is pink

• The ball is not pink

• If it is pink, then it is a ball

• If it is a ball, then it is pink

Answer explanation

The question asks for the negation of the statement 'The ball is not pink.' The negation of a statement is the opposite of that statement. In this case, the opposite of 'The ball is not pink' is 'The ball is pink.' Thus, the correct option is 'The ball is pink.'

Tags

G.4B

(Intermediate)

Write the negation of the statement.

p: The dog is not a Labrador Retriever.

~p: ​ (a)  

• The dog is a Labrador Retriever

• The dog is not a Labrador Retriever

• The dog is a Golden Retriever

• The cat is a tabby

Answer explanation

The statement p is 'The dog is not a Labrador Retriever'. The negation of this statement would be the opposite of it. Among the options, 'The dog is a Labrador Retriever' is the opposite and hence is the correct choice. The other options do not negate the original statement properly.

Tags

G.4B

• Inverse

• Contrapositive

• Converse

• Conditional

Tags

G.4B

• Inverse

• If it is February, then it is Valentine's Day.

• Contrapositive

• If it is not February, then it is not Valentine's Day.

• Converse

• If it is not Valentine's Day , then it is not February.

• Conditional

• If it is Valentine's Day , then it is February.

Tags

G.4B

• True, because congruent angles have the same degree measure

• False, because congruent angles add up to 180 degrees

• False, because congruent angles add up to 90 degrees

• False, because congruent angles are opposite degree measures.

Answer explanation

The question asks if angle S is congruent to angle T. The correct answer is 'True, because congruent angles have the same degree measure'. This statement is correct because by definition, congruent angles are angles that have the same degree measure. Therefore, if angle S is congruent to angle T, they must have the same degree measure.

Tags

G.4B

• False, because congruent angles add up to 90 degrees

• False, because congruent angles are opposite degree measures.

Answer explanation

The question asks whether the sum of two angles (angle 2 and angle 3) equals 180 degrees. The correct answer is 'True; if angles form a linear pair, then the sum of their angle measures is 180 degrees'. It suggests that when two angles form a linear pair, their sum is indeed 180 degrees. The other options incorrectly describe the properties of complementary and congruent angles.

Tags

G.4B

• True; M is the midpoint because it is the same distance from point A and point B

• True; the midpoint is between points A and B and lies on the same line

Answer explanation

The correct answer is 'False; the midpoint cannot be assumed unless AM and MB are marked as congruent.' In the question, we are asked to decide if there is enough information to confirm that M is the midpoint of line AB. While a midpoint is indeed equidistant from both endpoints, without specific markings indicating that AM is congruent to MB, we cannot confirm M's position as the midpoint.

Tags

G.4B