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A truth table problem.?
[(p then q)^(q then r)] then (p then r)
i couldn't find the arrow going right so i just wrote "then"
im in 8th grade if it means anything
1 Answer
- ?Lv 610 years agoFavorite Answer
Just write out your truth table. Since typesetting here is terrible, it won't be aligned properly, unfortunately.
p q r || p => q || q => r || (p => q) and (q => r) || (p => r) || ((p => q) and (q => r)) => (p => r)
F F F || T || T || T || T || T
F F T || T || T || T || T || T
F T F || T || F || F || T || T
F T T || T || T || T || T || T
T F F || F || T || F || F || T
T F T || F || T || F || T || T
T T F || T || F || F || F || T
T T T || T || T || T || T || T
Thus the proposition holds.
It's probably much easier to see without using a truth table, though. If p implies q and q implies r, the p implies r, since when p is true, q is true, and when q is true, r is true.
