Practice translating statements into logic, evaluating true and false expressions, using truth tables, and solving short logic puzzles.
Read each problem carefully. Use AND, OR, NOT, and IF...THEN to represent logical ideas. Show your reasoning in the space provided.
Use true and false statements to solve logic problems
CS - Grade 6-8
- 1
Let P mean 'It is raining' and Q mean 'I take an umbrella.' Write the statement 'If it is raining, then I take an umbrella' using P, Q, and IF...THEN.
- 2
Let P be true and Q be false. Is the statement P AND Q true or false? Explain your answer.
- 3
Let P mean 'The robot sees a wall' and Q mean 'The robot sees a hole.' What does P OR Q mean in words?
- 4
Let P mean 'The password is correct.' Write NOT P in words, then explain when NOT P is true.
- 5
Complete the truth table for P AND NOT Q. Use the row order: P true and Q true, P true and Q false, P false and Q true, P false and Q false.
- 6
For the statement IF P THEN Q, which row makes the whole statement false: P true and Q true, P true and Q false, P false and Q true, or P false and Q false?
- 7
Two students, A and B, are in a logic puzzle. Truth-tellers always tell the truth, and liars always lie. A says, 'B is a liar.' B says, 'A and I are the same type.' Determine who is a truth-teller and who is a liar.
- 8
A logic circuit has inputs P and Q. First, P and Q go into an AND gate. Then the result goes into a NOT gate. What expression does the circuit represent?
- 9
Use De Morgan's law to rewrite NOT (P AND Q) using OR and NOT.
- 10
A game door opens only if the player has a key AND has entered the secret code. Let K mean 'has a key' and C mean 'entered the secret code.' Write a logic expression for the door opening.
- 11
A rule says: 'If a number is divisible by 4, then it is even.' Write the converse of this statement and decide whether the converse is always true.
- 12
Evaluate the expression (P OR Q) AND R when P is false, Q is true, and R is true.
- 13
Complete the truth table for P OR (NOT Q). Use all four possible combinations of P and Q.
- 14
Three boxes are labeled A, B, and C. Exactly one box has a prize. The clues are: If the prize is in A, then clue 1 is true. Clue 1 says 'The prize is not in B.' Clue 2 says 'The prize is in C.' You learn that clue 2 is false. Which box has the prize?
- 15
A security system unlocks when K AND (C OR B) is true. K means 'the user has a key card,' C means 'the user knows the code,' and B means 'the user has a backup badge.' Will it unlock if K is true, C is false, and B is true? Explain.