Truth table verification 10
$begingroup$
The question:
Let $P$, $Q$, and $R$ be statements. Determine whether or not the two expressions in each pair are logically equivalent. In each case, demonstrate that your answer is correct.
a.) $(P ∧Q) ∧R, P ∧(Q ∧R)$
My attempt using truth table:
begin{array}{|c|c|c|c|}
hline
P& Q & P ∧ Q& R \ hline
T& T& T&T\ hline
F& T & F&F\ hline
T& F & F&F\ hline
F& F & F&F\ hline
end{array}
begin{array}{|c|c|c|c|}
hline
Q& R & Q ∧ R& P \ hline
T& T& T&T\ hline
F& T & F&F\ hline
T& F & F&F\ hline
F& F & F&F\ hline
end{array}
Therefore, they are equivelent.
Is this the correct method/approach to showing that the statements are correct using truth tables?
calculus proof-verification
asked Jan 8 at 22:57
ForextraderForextrader
717
$endgroup$
add a comment |
$begingroup$
The question:
Let $P$, $Q$, and $R$ be statements. Determine whether or not the two expressions in each pair are logically equivalent. In each case, demonstrate that your answer is correct.
a.) $(P ∧Q) ∧R, P ∧(Q ∧R)$
My attempt using truth table:
begin{array}{|c|c|c|c|}
hline
P& Q & P ∧ Q& R \ hline
T& T& T&T\ hline
F& T & F&F\ hline
T& F & F&F\ hline
F& F & F&F\ hline
end{array}
begin{array}{|c|c|c|c|}
hline
Q& R & Q ∧ R& P \ hline
T& T& T&T\ hline
F& T & F&F\ hline
T& F & F&F\ hline
F& F & F&F\ hline
end{array}
Therefore, they are equivelent.
Is this the correct method/approach to showing that the statements are correct using truth tables?
calculus proof-verification
asked Jan 8 at 22:57
ForextraderForextrader
717
$endgroup$
add a comment |
$begingroup$
The question:
Let $P$, $Q$, and $R$ be statements. Determine whether or not the two expressions in each pair are logically equivalent. In each case, demonstrate that your answer is correct.
a.) $(P ∧Q) ∧R, P ∧(Q ∧R)$
My attempt using truth table:
begin{array}{|c|c|c|c|}
hline
P& Q & P ∧ Q& R \ hline
T& T& T&T\ hline
F& T & F&F\ hline
T& F & F&F\ hline
F& F & F&F\ hline
end{array}
begin{array}{|c|c|c|c|}
hline
Q& R & Q ∧ R& P \ hline
T& T& T&T\ hline
F& T & F&F\ hline
T& F & F&F\ hline
F& F & F&F\ hline
end{array}
Therefore, they are equivelent.
Is this the correct method/approach to showing that the statements are correct using truth tables?
calculus proof-verification
asked Jan 8 at 22:57
ForextraderForextrader
717
$endgroup$
The question:
Let $P$, $Q$, and $R$ be statements. Determine whether or not the two expressions in each pair are logically equivalent. In each case, demonstrate that your answer is correct.
a.) $(P ∧Q) ∧R, P ∧(Q ∧R)$
My attempt using truth table:
begin{array}{|c|c|c|c|}
hline
P& Q & P ∧ Q& R \ hline
T& T& T&T\ hline
F& T & F&F\ hline
T& F & F&F\ hline
F& F & F&F\ hline
end{array}
begin{array}{|c|c|c|c|}
hline
Q& R & Q ∧ R& P \ hline
T& T& T&T\ hline
F& T & F&F\ hline
T& F & F&F\ hline
F& F & F&F\ hline
end{array}
Therefore, they are equivelent.
Is this the correct method/approach to showing that the statements are correct using truth tables?
calculus proof-verification
calculus proof-verification
asked Jan 8 at 22:57
ForextraderForextrader
717
asked Jan 8 at 22:57
ForextraderForextrader
717
asked Jan 8 at 22:57
ForextraderForextrader
717
asked Jan 8 at 22:57
ForextraderForextrader
717
asked Jan 8 at 22:57
ForextraderForextrader
717
717
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
It is correct. Although, you might use the fact that $land$ is associative unless the problem specifically doesn't want you to do that. If that is the case, then the truth table is the only way.
answered Jan 8 at 23:01
EuxhenHEuxhenH
482210
$endgroup$
$begingroup$
Thank you, yes the professor had said to use truth tables.
$endgroup$
– Forextrader
Jan 8 at 23:02
$begingroup$
@Forextrader Just to make the answer more complete, add one more column in the end for both tables, that includes the full expressions.
$endgroup$
– EuxhenH
Jan 8 at 23:04
$begingroup$
Ah that's a good thought. Thank you
$endgroup$
– Forextrader
Jan 8 at 23:05
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
It is correct. Although, you might use the fact that $land$ is associative unless the problem specifically doesn't want you to do that. If that is the case, then the truth table is the only way.
answered Jan 8 at 23:01
EuxhenHEuxhenH
482210
$endgroup$
$begingroup$
Thank you, yes the professor had said to use truth tables.
$endgroup$
– Forextrader
Jan 8 at 23:02
$begingroup$
@Forextrader Just to make the answer more complete, add one more column in the end for both tables, that includes the full expressions.
$endgroup$
– EuxhenH
Jan 8 at 23:04
$begingroup$
Ah that's a good thought. Thank you
$endgroup$
– Forextrader
Jan 8 at 23:05
add a comment |
$begingroup$
It is correct. Although, you might use the fact that $land$ is associative unless the problem specifically doesn't want you to do that. If that is the case, then the truth table is the only way.
answered Jan 8 at 23:01
EuxhenHEuxhenH
482210
$endgroup$
$begingroup$
Thank you, yes the professor had said to use truth tables.
$endgroup$
– Forextrader
Jan 8 at 23:02
$begingroup$
@Forextrader Just to make the answer more complete, add one more column in the end for both tables, that includes the full expressions.
$endgroup$
– EuxhenH
Jan 8 at 23:04
$begingroup$
Ah that's a good thought. Thank you
$endgroup$
– Forextrader
Jan 8 at 23:05
add a comment |
$begingroup$
It is correct. Although, you might use the fact that $land$ is associative unless the problem specifically doesn't want you to do that. If that is the case, then the truth table is the only way.
answered Jan 8 at 23:01
EuxhenHEuxhenH
482210
$endgroup$
It is correct. Although, you might use the fact that $land$ is associative unless the problem specifically doesn't want you to do that. If that is the case, then the truth table is the only way.
answered Jan 8 at 23:01
EuxhenHEuxhenH
482210
answered Jan 8 at 23:01
EuxhenHEuxhenH
482210
answered Jan 8 at 23:01
EuxhenHEuxhenH
482210
answered Jan 8 at 23:01
EuxhenHEuxhenH
482210
482210
$begingroup$
Thank you, yes the professor had said to use truth tables.
$endgroup$
– Forextrader
Jan 8 at 23:02
$begingroup$
@Forextrader Just to make the answer more complete, add one more column in the end for both tables, that includes the full expressions.
$endgroup$
– EuxhenH
Jan 8 at 23:04
$begingroup$
Ah that's a good thought. Thank you
$endgroup$
– Forextrader
Jan 8 at 23:05
add a comment |
$begingroup$
Thank you, yes the professor had said to use truth tables.
$endgroup$
– Forextrader
Jan 8 at 23:02
$begingroup$
@Forextrader Just to make the answer more complete, add one more column in the end for both tables, that includes the full expressions.
$endgroup$
– EuxhenH
Jan 8 at 23:04
$begingroup$
Ah that's a good thought. Thank you
$endgroup$
– Forextrader
Jan 8 at 23:05
$begingroup$
Thank you, yes the professor had said to use truth tables.
$endgroup$
– Forextrader
Jan 8 at 23:02
$begingroup$
Thank you, yes the professor had said to use truth tables.
$endgroup$
– Forextrader
Jan 8 at 23:02
$begingroup$
@Forextrader Just to make the answer more complete, add one more column in the end for both tables, that includes the full expressions.
$endgroup$
– EuxhenH
Jan 8 at 23:04
$begingroup$
@Forextrader Just to make the answer more complete, add one more column in the end for both tables, that includes the full expressions.
$endgroup$
– EuxhenH
Jan 8 at 23:04
$begingroup$
Ah that's a good thought. Thank you
$endgroup$
– Forextrader
Jan 8 at 23:05
$begingroup$
Ah that's a good thought. Thank you
$endgroup$
– Forextrader
Jan 8 at 23:05
add a comment |
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