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please provide an inverse and contrapositive statement to these two statements:

1. If it rains, then the ground will be wet. If the ground is wet, then it rains.
2. if I'm fishing then I'm happy. if I'm happy then I'm fishing

1 answer

Sure! Let's break down each of the two statements and then derive their inverse and contrapositive.

1. Statement:

  • "If it rains, then the ground will be wet."
  • "If the ground is wet, then it rains."

Inverse:

  • "If it does not rain, then the ground will not be wet."
  • "If the ground is not wet, then it does not rain."

Contrapositive:

  • "If the ground is not wet, then it does not rain."
  • "If it is not true that the ground is wet, then it does not rain."

2. Statement:

  • "If I'm fishing, then I'm happy."
  • "If I'm happy, then I'm fishing."

Inverse:

  • "If I'm not fishing, then I'm not happy."
  • "If I'm not happy, then I'm not fishing."

Contrapositive:

  • "If I'm not happy, then I'm not fishing."
  • "If I'm not fishing, then I'm not happy."

In summary:

  1. For "If it rains, then the ground will be wet," the inverse is "If it does not rain, then the ground will not be wet," and the contrapositive is "If the ground is not wet, then it does not rain."
  2. For "If I'm fishing, then I'm happy," the inverse is "If I'm not fishing, then I'm not happy," and the contrapositive is "If I'm not happy, then I'm not fishing."