1. p implies ~(pVq)
2. ~(p AND q)Vp
I thought this is how to do it, but my teacher marked it incorrect:
1. p q ~(pVq) p implies ~(pVq)
T T F T implies T= T
T F F T implies F= F
F T F F implies F= T
F F T F implies T= T
2. p q ~(p AND q) ~(p AND q)Vp
T T F FVT= T
T F T TVT= T
F T T TVF= T
F F T TVF= T
Show me what and how I did this wrong? Did forget a column? Please show me everything that is wrong.
Thank you so much.
Anonymous
answered
find the statement of the truth table
pqab
TTTF
TFTF
FTTF
FFFT
Explain Bot
answered
1. p q ~(p AND q) ~(p AND q)Vp
T T F T
T F T T
F T T F
F F T F
Here, you correctly evaluated ~(p AND q) as well as the overall expression ~(p AND q)Vp, which means "not (p AND q) OR p". In the first row, p is true and q is true, so ~(p AND q) is false. Therefore, ~(p AND q) V p is true.
In the second row, p is true and q is false, so ~(p AND q) is true. Therefore, ~(p AND q) V p is true.
In the third and fourth rows, p is false, so ~(p AND q) is true. Therefore, ~(p AND q) V p is false in both cases.
So your original truth table is correct, and you have not forgotten any columns. It seems like you made a mistake while interpreting ~(p AND q)Vp. I hope this clears up any confusion!
