Mathematical Statement, Connectives, truth Value and Negation

Which of the following is a mathematical statement?

• If you are lucky and you know it, clap your hands.

• Are you clapping your hands?

• You know it if and only if you are clapping your hands.

• Clapping hands is lucky.

• False

• True

• True

• False

• s can either be True or False

• the statement cannot be true for any truth value of s

What truth values should be in (1), (2) and (3)?

• T, T, T

• T, F, F

• F, T, T

• F, F, F

Answer explanation

The ____________ is true if both 𝑝 and 𝑞 are true. Otherwise, it is false.

What is the correct negation of the following statement?

" Some UP students do not have a smartphone. "

• All UP students have a smartphone.

• No UP student have a smartphone.

• Some UP students have a smartphone.

• All UP students do not have a smartphone.

What is the correct negation of the statement:

" Lily has more than 40 pad papers. "

• Lily has less than 40 pad papers.

• Lily has at most 40 pad papers.

• Lily has at least 40 pad papers.

• Lily has no pad papers.

What is the correct negation of the statement:

" She will pass the exam or she will not have a new iPad. "

• She will not pass the exam and she will not have a new iPad.

• She will pass the exam and she will have a new iPad.

• She will not pass the exam or she will not have a new iPad.

• She will not pass the exam and she will have a new iPad.

Which of the following is NOT an implication?

• If it is a square, then it is a paralllogram.

• If it is a parallelogram, then it is a square.

• If the polygon has five sides, then it is a pentagon.

• If the polygon is a pentagon, then it is has five sides.