Write the if-then statement that follows from the pair of true statements
If I go to the movie, then I will stay up late
If I stay up late, then I will be tired tomorrow
by transitivity,
movie -> late & late -> tired
if movie, then tired.
The if-then statement that follows from the pair of true statements is:
"If I go to the movie, then I will be tired tomorrow."
To understand how this statement is derived, we can break it down based on the original pair of true statements:
1. "If I go to the movie, then I will stay up late."
2. "If I stay up late, then I will be tired tomorrow."
If we combine these statements, we can substitute the second half of the first statement with the first half of the second statement:
"If I go to the movie, then I will (stay up late and) be tired tomorrow."
However, since it is redundant to mention staying up late twice in the same statement, we can simplify it to:
"If I go to the movie, then I will be tired tomorrow."