"Only If" and Necessary and Sufficient Conditions: The sentences below illustrate the use of necessary and sufficient conditions and "only if." To symbolize these sentences successfully it is usually best to rely on the "rules" associated with each concept. Be sure to check the help screen for important info about symbolization exercises.
You can SPEAK the truth only if you KNOW the truth.
K→S
S→K
Janet makes APRICOT jello only if it's TUESDAY, but she makes BLACK cherry jello only when it's WEDNESDAY.
(T→>A)&(W→B)
(A&B)→(T&W)
(A→T)&(B→W)
The magic WORKS only when the victim BELIEVES in it.
W→B
B→W
Only if she offers the MOON, will I request the SUN.
M→S
S→M
Only in the event that the creatures are both HIDEOUS and DESPICABLE will they sell video GAMES.
G&(H→D)
(H&D)→G
G→(H→D)
G→(H&D)
If they serve JELLO, you should TRY it only if it's properly CHILLED.
J→(T→C)
C→(J→T)
(J→T)→C
J→(C→T)
A sufficient condition for BURNING paper is a TEMPERATURE of 451 degrees farhenheit.
B→T
T→B
EGGS are necessary for an OMELETTE.
E→O
O→E
If WORKING towards a goal is necessary for SUCCESS and success is essential for HAPPINESS, then you'll have happiness only if you work towards a goal.
((W→S)&(S→H))→(W→H)
((W→S)&(S→H))→(H→W)
(W→H)→((W→S)&(S→H))
((S→W)&(H→S))→(H→W)
Given that quality MUSIC is necessary for a RICH and SATISFYING life, you can be HAPPY only if you listen to DYLAN and the BEATLES.