"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.

The CREATURES will attack only if PROVOKED.
1. C→P
2. P→C
You can SPEAK the truth only if you KNOW the truth.
1. S→K
2. K→S
Janet makes APRICOT jello only if it's TUESDAY, but she makes BLACK cherry jello only when it's WEDNESDAY.
1. (A→T)&(B→W)
2. (T→>A)&(W→B)
3. (A&B)→(T&W)
The magic WORKS only when the victim BELIEVES in it.
1. W→B
2. B→W
It HURTS only when I LAUGH.
1. H→L
2. L→H
Only if she offers the MOON, will I request the SUN.
1. S→M
2. M→S
Only supposing that bunnies are DELICIOUS, should they be EATEN.
1. E→D
2. D→E
Only provided that TRUTH and MEANING are illusory, should you PANIC.
1. P→(T&M)
2. (T&M)→P
3. T&(M→P)
4. P→(T→M)
Only in the event that the creatures are both HIDEOUS and DESPICABLE will they sell video GAMES.
1. G→(H&D)
2. (H&D)→G
3. G&(H→D)
4. G→(H→D)
Only in the event that the characters are both HIDEOUS and DESPICABLE will they sell video GAMES.
1. G→(H&D)
2. (H&D)→G
3. G&(H→D)
4. G→(H→D)
If they serve JELLO, you should TRY it only if it's properly CHILLED.
1. J→(T→C)
2. J→(C→T)
3. (J→T)→C
4. C→(J→T)
When civilization COLLAPSES, we will eat JELLO only when we're LUCKY.
1. C→(J→L)
2. C→(L→J)
3. (J→L)→C
4. L→(C→J)
RAISING the temperature to 100 degrees celsius is a sufficient condition for BOILING water.
1. R→B
2. B→R
A sufficient condition for BURNING paper is a TEMPERATURE of 451 degrees farhenheit.
1. T→B
2. B→T
Thinking about the KITTENS and the trash COMPACTOR is sufficient to make her SHIVER.
1. (K&C)→S
2. S→(K&C)
3. S→(K→C)
4. S→(C→K)
To make him LAUGH it is enough to remind him of the SALAMANDERS and the FORK.
1. (S&F)→L
2. L→(S&F)
3. (S→F)→L
4. L&S&F
EGGS are necessary for an OMELETTE.
1. O→E
2. E→O
For human LIFE, CARBON, OXYGEN, and refreshing DESSERTS are all required.
1. L→(C&O&D)
2. (C&O&D)→L
3. L&C&O&D
4. D→(L&C&O)
Essential for BELIEF is FAITH, but essential for faith is REVELATION.
1. (B→F)&(F→R)
2. B→(F→R)
3. (F→B)&(R→F)
4. (F&R)→B
The mandatory course distribution for GRADUATION includes both HUMANITIES and SCIENCES.
1. G→(H&S)
2. (H&S)→G
3. G&H&S
4. (H→S)→G
Although CANDLES are necessary for a ROMANTIC dinner, BURNING down the house is sufficient to SPOIL the mood.
1. (R→C)&(B→S)
2. (C→R)&(B→S)
3. (R→C)&(S→B)
4. (C→R)&(S→B)
For acknowledging her PREVIOUS work a THANK you is adequate, however, a pay RAISE is required to assure FUTURE performance.
1. (T→P)&(F→R)
2. (P→T)&(R→F)
3. (P→T)&(F→R)
4. (T→P)&(R→F)
While READING and THINKING are sufficient preparation for many college CLASSES, for LOGIC, putting PENCIL to paper is essential.
1. ((R&T)→C)&(L→P)
2. (C→(R&T))&(P→L)
3. ((R&T)→C)&(P→L)
4. (C→(R&T))&(L→P)
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.
1. ((S→W)&(H→S))→(H→W)
2. ((W→S)&(S→H))→(H→W)
3. ((W→S)&(S→H))→(W→H)
4. (W→H)→((W→S)&(S→H))
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.
1. ((R&S)→M)→(H→(D&B))
2. (M→(R&S))→(H→(D&B))
3. ((R&S)→M)→((D&B)→H)
4. (R&S)→((M&H)→(D&B))
If existence is intrinsically PARADOXICAL and hopelessly WEIRD, then you can UNDERSTAND the world only if you reject LOGIC and RATIONALITY.
1. (P&W)→(U→(L&R))
2. (P&W)→((L&R)→U)
3. (U→(L&R))→(P&W)
4. ((L&R)→U)→(P&W)
You should do AEROBIC activity daily, supposing that regular EXERCISE is necessary for both PHYSICAL and MENTAL health.
1. ((P&M)→E)→A
2. A→((P&M)→E)
3. A→(E→(P&M))
4. (E→(P&M))→A
Reading NIETZSCHE and DESCARTES is necessary for a good LIFE, only assuming that studying PHILOSOPHY is required for HAPPINESS.
1. (L→(N&D))→(H→P)
2. ((N&D)→L)→(P→H)
3. ((N&D)→L)→(H→P)
4. (N&D)→((H→P)→L)
Only if reflection on one's HISTORY and CULTURE is necessary for a MEANINGFUL existence, is studying ART and LITERATURE essential for a SATISFYING life.
1. (S→(A&L))→(M→(H&C))
2. ((A&L)→S)→(M→(H&C))
3. (M→(H&C))→(S→(A&L))
4. (M→(H&C))→((A&L)→S)
Only when CORN flakes are sufficient for KNOWLEDGE and RICE crispies are sufficient for WISDOM, is BREAKFAST cereal adequate for UNDERSTANDING.
1. (B→U)→((C→K)&(R→W))
2. ((C→K)&(R→W))→(B→U)
3. (B→U)→((C→K)&(R→W))
4. ((C→K)&(R→W))→(U→B)
Only provided that DRAGONS and ELVES are necessary for the PLOT, is an enchanted FOREST mandatory for the SETTING.
1. (S→F)→(P→(D&E))
2. (F→S)→((D&E)→P)
3. (P→(D&E))→(S→F)
4. (P→(D&E))→(F→S)