Mathematical Logic: Statements and Validity

Which of the following sentences is a statement?

Identify the compound statment

Which logical connective represents 'if and only if'?

Which logical connective is used to represent 'and'?

The statement 'It is not the case that today is both sunny and cold' can be represented symbolically as?

What is the symbolic representation of 'If it rains, then the game is canceled'?

Given the propositions P: 'The cat is sleeping' and Q: 'The dog is barking', how would you represent 'The cat is sleeping or the dog is not barking'?

Which of the following correctly expresses “P only if Q”?

Which of the following is the converse of the statement 'If it is raining, then the ground is wet'?

Given P represents 'It is raining' and Q represents 'I will take an umbrella,' which expression symbolizes 'If it is not raining, then I will not take an umbrella'?

Let A = 'The sun is shining' and B = 'The birds are singing'. What is the symbolic representation of 'The sun is not shining, but the birds are singing'?

If P represents 'The cake is chocolate' and Q represents 'The frosting is vanilla', how would you symbolically write 'Either the cake is chocolate, or the frosting is vanilla, but not both'?

Consider P: 'I exercise daily' and Q: 'I feel healthy'. Which statement corresponds to $P \leftrightarrow Q$?

Given the statement 'If it snows, then school is canceled,' which of the following is its contrapositive?

Let 'p' represent 'The printer is out of paper,' and 'q' represent 'The printer is not working'. How would you express 'The printer is not out of paper and is working' symbolically?

Which of the following is logically equivalent to $P \rightarrow Q$?

If statement A is 'The car is red' and statement B is 'The car is fast', how would you represent 'The car is red or the car is not fast'?

Given the propositions P: 'The computer is on' and Q: 'The internet is down', express 'The computer is on unless the internet is down' symbolically.

If P symbolizes 'The train is late' and Q symbolizes 'I will miss my appointment', how would you represent 'If the train is late, then I will miss my appointment, and the train is late'?

Which of the expressions below accurately symbolizes: 'You can access the network only if you have a valid password'?

Suppose X is 'The flowers are blooming' and Y is 'The bees are buzzing'. Choose the symbolic form best representing 'The flowers are blooming unless the bees are not buzzing'.

Let P be 'The code compiles' and Q be 'The program runs'. Select the symbolic representation that matches 'The code compiles, or if the program doesn’t run, then the code doesn't compile'.

Given: R = 'The road is icy', D = 'Driving is dangerous.' Express 'The road is not icy if and only if driving is not dangerous' in symbolic form.

If 'm' stands for 'Maria sings' and 'j' stands for 'John dances', how is 'Maria sings if John dances' written symbolically?

Given 'r' represents 'The report is finished' and 's' represents 'The presentation is ready,' how would you symbolize 'The report is not finished unless the presentation is ready'?

Let C = 'The sky is cloudy' and R = 'It is raining.' Select the symbolic form representing: 'If the sky is cloudy, then it is raining, but it is not raining'.