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Suppose that the converse of the conditional statement 201cif it rained last night, then the sidewalk is wet.201d is false. which of the other statements has to be false as well?, A. if the sidewalk is not wet, then it did not rain last night., B. if it did not rain last night, then the sidewalk is not wet., C. if the sidewalk is wet, then it rained last night., D. if it rained last night, then the sidewalk is wet.

Written by Winona · 43 sec read >


Suppose that the converse of the conditional statement “if it rained last night, then the sidewalk is wet.” is false. which of the other statements has to be false as well?


A. if the sidewalk is not wet, then it did not rain last night.
B. if it did not rain last night, then the sidewalk is not wet.
C. if the sidewalk is wet, then it rained last night.
D. if it rained last night, then the sidewalk is wet.​

“Answer is Letter C”

C. if the sidewalk is wet, then it rained last night

Conditional Statement:

If p, then q

p- it rained last night

q– the sidewalk is wet

Example:

  • If it rained last night, then the sidewalk is wet

Converse Statement:

If q, then p

pit rained last night

qthe sidewalk is wet

Example:

  • If the sidewalk is wet, then it rained last night

Inverse Statement:

If not p,then not q

p- it rained last night

qthe sidewalk is wet

Example:

  • If it did not rain last night, then the sidewalk is not wet.

Contrapositive Statement:

If not q,then not p

p- it rained last night

q- the sidewalk is wet

Example:

  • If the sidewalk is not wet, then it did not rain last night.

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