Mixing
Show that $((pLeftrightarrow q)Leftrightarrow T)$ and $(pLeftrightarrow (qLeftrightarrow T))$ are logically...
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I tried this but I'm not sure what to do about the T value:
$$((pLeftrightarrow q ) Leftrightarrow T ) equiv neg p Leftrightarrow neg q Leftrightarrow T equiv neg p Leftrightarrow neg (neg q Leftrightarrow neg T) equiv neg p Leftrightarrow (q Leftrightarrow T)$$
Am I using the rules correctly?
logic propositional-calculus
asked Jan 29 at 18:58
memelord420xdmemelord420xd
61
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add a comment |
$begingroup$
I tried this but I'm not sure what to do about the T value:
$$((pLeftrightarrow q ) Leftrightarrow T ) equiv neg p Leftrightarrow neg q Leftrightarrow T equiv neg p Leftrightarrow neg (neg q Leftrightarrow neg T) equiv neg p Leftrightarrow (q Leftrightarrow T)$$
Am I using the rules correctly?
logic propositional-calculus
asked Jan 29 at 18:58
memelord420xdmemelord420xd
61
$endgroup$
1
$begingroup$
How about a truth table?
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– Umberto P.
Jan 29 at 19:03
$begingroup$
I already did the truth table for question A but B asks to do it with transformations
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– memelord420xd
Jan 29 at 21:11
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@memelord420xd what transformation rules do you have available?
$endgroup$
– Bram28
Feb 1 at 1:48
add a comment |
$begingroup$
I tried this but I'm not sure what to do about the T value:
$$((pLeftrightarrow q ) Leftrightarrow T ) equiv neg p Leftrightarrow neg q Leftrightarrow T equiv neg p Leftrightarrow neg (neg q Leftrightarrow neg T) equiv neg p Leftrightarrow (q Leftrightarrow T)$$
Am I using the rules correctly?
logic propositional-calculus
asked Jan 29 at 18:58
memelord420xdmemelord420xd
61
$endgroup$
I tried this but I'm not sure what to do about the T value:
$$((pLeftrightarrow q ) Leftrightarrow T ) equiv neg p Leftrightarrow neg q Leftrightarrow T equiv neg p Leftrightarrow neg (neg q Leftrightarrow neg T) equiv neg p Leftrightarrow (q Leftrightarrow T)$$
Am I using the rules correctly?
logic propositional-calculus
logic propositional-calculus
asked Jan 29 at 18:58
memelord420xdmemelord420xd
61
asked Jan 29 at 18:58
memelord420xdmemelord420xd
61
edited Jan 29 at 21:13
memelord420xd
asked Jan 29 at 18:58
memelord420xdmemelord420xd
61
asked Jan 29 at 18:58
memelord420xdmemelord420xd
61
asked Jan 29 at 18:58
memelord420xdmemelord420xd
61
61
1
$begingroup$
How about a truth table?
$endgroup$
– Umberto P.
Jan 29 at 19:03
$begingroup$
I already did the truth table for question A but B asks to do it with transformations
$endgroup$
– memelord420xd
Jan 29 at 21:11
$begingroup$
@memelord420xd what transformation rules do you have available?
$endgroup$
– Bram28
Feb 1 at 1:48
add a comment |
1
$begingroup$
How about a truth table?
$endgroup$
– Umberto P.
Jan 29 at 19:03
$begingroup$
I already did the truth table for question A but B asks to do it with transformations
$endgroup$
– memelord420xd
Jan 29 at 21:11
$begingroup$
@memelord420xd what transformation rules do you have available?
$endgroup$
– Bram28
Feb 1 at 1:48
1
1
$begingroup$
How about a truth table?
$endgroup$
– Umberto P.
Jan 29 at 19:03
$begingroup$
How about a truth table?
$endgroup$
– Umberto P.
Jan 29 at 19:03
$begingroup$
I already did the truth table for question A but B asks to do it with transformations
$endgroup$
– memelord420xd
Jan 29 at 21:11
$begingroup$
I already did the truth table for question A but B asks to do it with transformations
$endgroup$
– memelord420xd
Jan 29 at 21:11
$begingroup$
@memelord420xd what transformation rules do you have available?
$endgroup$
– Bram28
Feb 1 at 1:48
$begingroup$
@memelord420xd what transformation rules do you have available?
$endgroup$
– Bram28
Feb 1 at 1:48
add a comment |
1 Answer
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Hint: $quad r equiv (rleftrightarrow top)$
answered Jan 29 at 23:06
Graham KempGraham Kemp
87.6k43578
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1 Answer
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1 Answer
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$begingroup$
Hint: $quad r equiv (rleftrightarrow top)$
answered Jan 29 at 23:06
Graham KempGraham Kemp
87.6k43578
$endgroup$
add a comment |
$begingroup$
Hint: $quad r equiv (rleftrightarrow top)$
answered Jan 29 at 23:06
Graham KempGraham Kemp
87.6k43578
$endgroup$
add a comment |
$begingroup$
Hint: $quad r equiv (rleftrightarrow top)$
answered Jan 29 at 23:06
Graham KempGraham Kemp
87.6k43578
$endgroup$
Hint: $quad r equiv (rleftrightarrow top)$
answered Jan 29 at 23:06
Graham KempGraham Kemp
87.6k43578
answered Jan 29 at 23:06
Graham KempGraham Kemp
87.6k43578
answered Jan 29 at 23:06
Graham KempGraham Kemp
87.6k43578
answered Jan 29 at 23:06
Graham KempGraham Kemp
87.6k43578
87.6k43578
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$begingroup$
How about a truth table?
$endgroup$
– Umberto P.
Jan 29 at 19:03
$begingroup$
I already did the truth table for question A but B asks to do it with transformations
$endgroup$
– memelord420xd
Jan 29 at 21:11
$begingroup$
@memelord420xd what transformation rules do you have available?
$endgroup$
– Bram28
Feb 1 at 1:48