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Worksheet: Determine Truth Values of Negations, Conjunctions, and Disjunctions

Q1:

Let 𝐴 be the hypothesis β€œ π‘₯ + 3 = 3 + π‘₯ ” and 𝐡 be the conclusion β€œ π‘₯ is prime.”

The conditional statement 𝐴 β‡’ 𝐡 reads, β€œIf π‘₯ + 3 = 3 + π‘₯ , then π‘₯ is prime.” Is this true or false?

  • AFalse
  • BTrue

The converse statement 𝐡 β‡’ 𝐴 reads, β€œIf π‘₯ is prime, then π‘₯ + 3 = 3 + π‘₯ .” Is this true or false?

  • ATrue
  • BFalse

The inverse statement Β¬ 𝐴 β‡’ Β¬ 𝐡 reads, β€œIf π‘₯ + 3 β‰  3 + π‘₯ , then π‘₯ is not prime.” Is this true or false?

  • AFalse
  • BTrue

The contrapositive statement Β¬ 𝐡 β‡’ Β¬ 𝐴 reads, β€œIf π‘₯ is not prime, then π‘₯ + 3 β‰  3 + π‘₯ .” Is this true or false?

  • ATrue
  • BFalse

Q2:

Which of the following is the inverse of the conditional statement β€œIf the measures of all the internal angles of a polygon are at most 180 degrees, then the polygon is convex?”

  • AIf a polygon is convex, then the measures of all the internal angles are at most 180 degrees.
  • BIf a polygon is not convex, then one of its internal angles measures more than 180 degrees.
  • CIf one of the internal angles of a polygon measures more than 180 degrees, then the polygon is not convex.

Q3:

Consider the conditional statement β€œIf 𝐴 , then 𝐡 ,” where the hypothesis 𝐴 is β€œ π‘₯ and 𝑦 are even numbers” and the conclusion 𝐡 is β€œ π‘₯ + 𝑦 is even.”

Statement If 𝐴 , then 𝐡 . If 𝐡 , then 𝐴 . If not 𝐴 , then not 𝐡 . If not 𝐡 , then not 𝐴 .
True or False

Complete the table to give the truth value of the conditional statement and its converse, inverse, and contrapositive.

  • ATrue, False, False, False
  • BTrue, True, False, True
  • CFalse, False, False, True
  • DTrue, False, False, True
  • EFalse, False, True, True