Propositions and Symbols

What is the word used to join the statements in disjunction form?

• And

• Or

• If...then

• If and only if

Let p be the statement: “Sam is a senior high school student” and let q be “Sam is over 15 years old”. Under which condition is the statement: “Sam is neither a senior high school student nor over 15 years old” true?

• ~ p ˄ q is true when at least one of p and q is false.

• ~ p ˄ q is true when at least one of p and q are true.

• ~ p ˄ ~ q is true when both p and q are false.

• ~ p ˄ ~ q is true when both p and q are true.

What is the bi- conditional of this statement?

"Parallel lines do not intersect."

• Two lines do not intersect if and only if they are parallel.

• Two lines are parallel if and only if they intersect.

• Two lines are not parallel if and only if they do not intersect .

• Two lines are parallel if and only if they do not intersect.

Which of the following option is true?

• 3 +2 = 8 if 5-2 = 7

• 1 > 3 and 3 is a positive integer

• -2 > 3 or 3 is a negative integer

• If the Sun is a planet, pigs will fly.

Let p and q represent the following simple statements: “p: Jing likes hotdog” and “q: Jing likes bacon.”

What is the symbolic form of the following statement: “Jing doesn’t like hotdog and bacon.”

• ~ (p ˄ q)

• p ˄ ~q

• p → q

• ~ ( p ˅ q)

Which of the following is TRUE about statement or proposition?

• It is a declarative sentence. It is TRUE but can’t be FALSE

• It is a declarative sentence. It can be both TRUE or FALSE.

• It is a declarative sentence. It is neither TRUE or FALSE.

• It is a declarative sentence. It is either TRUE or FALSE, but NOT BOTH.

Which of the following logic connectives is equivalent to ~ (p → q)?

• P ˅ ~q

• P ˄ ~q

• ~p ˅ ~q

• ~ p ˄ ~q

Write the following statement in p ↔ q form: “Perpendicular lines intersect at a right angle.”

• Two lines intersect at a right angle if and only if they are perpendicular lines.

• Perpendicular lines intersect if and only if at a right angle.

• Two lines are perpendicular if and only if they intersect at a right angle.

• Two lines intersect at a right angle if and only if they are perpendicular lines.

What is the negation of the statement, “A circle has a diameter of 14 cm.”?

• A circle doesn’t have a diameter of 14 cm.

• A circle has no diameter of 14 cm.

• A circle hasn’t a diameter of 14 cm.

• A circle is not 14 cm.

Which is NOT true about conjunction?

• The statement is true if both p and q are FALSE, otherwise it is FALSE.

• The statement is true if both p and q are TRUE, otherwise it is FALSE.

• The statement is false if both p and q are TRUE, otherwise it is FALSE.

• The statement is formed by using the word “and”.