3.5 Boolean Expressions

Amy wants to send an invitation to join the soccer team to all of the senior girls who are not already on the tennis team.  The variable female is true for girls and false for boys.  The variable grade equals the students grade (12 for seniors).  The variable tennis is true for members of the tennis team, otherwise it is false.  Which of the following Boolean expressions will evaluate true for only those students that Amy should send the invitation to?

• (female AND tennis) OR (grade = 12)

• NOT (female AND (grade = 12)) AND tennis

• (female AND (grade = 12)) AND (NOT tennis)

• (NOT tennis) OR (female AND (grade = 12))

A AND (B OR NOT C)

If the value of A is true and the value of the expression above is false, then what are the values of B and C?

• B is false and C is true

• B is true and C is false

• B and C are both true

• B and C are both false

A child’s mother will not allow him to have dessert if his chores were not completed.  He also cannot have dessert if he got in trouble at school and got detention.  But he is always allowed to have dessert on his birthday.  Which of the following expression will correctly evaluate to true if the child is allowed to have dessert?

• (NOT detention) AND (chores_complete OR birthday)

• (chores_complete AND birthday) OR (NOT detention)

• (NOT detention AND chores_complete) OR birthday

• NOT (detention AND chores_complete) OR birthday

A ← True

B ← False

C ← False

Which of the following Boolean expressions will evaluate to True?

Select two answers.

• A AND NOT (B OR C)

• (A AND B) OR NOT C

• NOT A AND (B OR C)

• (A OR B) AND C

Given that B is false, then which of these describes the possible values for the output?

• The output will be true if A and C are both true.

• The output will be true if A is false and C is true.

• The output will be true if A and C are both false.

• The output cannot be true.

Which of the following statements is equivalent to the algorithm in the flowchart?

• y ← NOT (x < 5 AND z > 10)

• y ← NOT (x < 5 OR z > 10)

• y ← x < 5 AND (NOT z > 10)

• y ← x < 5 AND z > 10

Which of these expressions is equivalent to expression C in the table?

• NOT (A OR B)

• (NOT A) AND B

• A AND B

• A OR (NOT B)