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Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements. Statements: Some snakes are lizards. All roosters are lizards. Conclusions: (I) All lizards are roosters. (II) No roosters are snakes.
Both conclusions (I) and (II) follow.
Only conclusion (I) follows.
Neither conclusion (I) nor (II) follows.
Only conclusion (II) follows.
Neither conclusion (I) nor (II) follows.
Convert statements into standard Venn/Euler diagram or positive/negative premise rules: Two positive premises (Some + All) can never yield a negative conclusion. Also, 'All roosters are lizards' gives the conversion 'Some lizards are roosters', not 'All lizards are roosters'.
Convert statements into standard Venn/Euler diagram or positive/negative premise rules: Two positive premises (Some + All) can never yield a negative conclusion. Also, 'All roosters are lizards' gives the conversion 'Some lizards are roosters', not 'All lizards are roosters'.
Analyze Statement 1
Statement 1: 'Some snakes are lizards' is an I-type (Particular Affirmative) proposition. It means the intersection of snakes and lizards is non-empty.
Analyze Statement 2
Statement 2: 'All roosters are lizards' is an A-type (Universal Affirmative) proposition. The set of roosters is completely inside the set of lizards.
Evaluate Conclusion I
Conclusion I: 'All lizards are roosters.' Since 'All roosters are lizards' gives the converse 'Some lizards are roosters', the universal conversion 'All lizards are roosters' is false.
Evaluate Conclusion II
Conclusion II: 'No roosters are snakes.' Both given statements are positive (affirmative). Two positive statements can never produce a negative conclusion in standard syllogism rules.
A: Both conclusions do not follow because Conclusion I and II are both logically invalid. B: Only conclusion (I) is wrong because universal conversion of 'All' is invalid. D: Only conclusion (II) is wrong because two positive premises cannot yield a negative conclusion.
C is correct because neither conclusion follows: Conclusion I is an invalid universal conversion from a particular premise, and Conclusion II is a negative conclusion derived from two positive premises.
Remember the golden rule of syllogism: From positive statements, no negative conclusion can ever be definitively drawn.
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