Competitive Exams : Reasoning Ability - Syllogism (Set 1) | Concept of Maths

Question 1

1. Determine which of the conclusions logically follow from the given statements.

A) Only conclusion I follows

B) Only conclusion II follows

C) Either I or II follows

D) Neither I nor II follows

Answer

Correct Answer: B

Solution: Let $NN$ = Neural Networks, $S$ = Synapses, and $N$ = Neurons. 1. "Only a few $NN$ are $S$" means:    - Some $NN$ are $S$.    - Some $NN$ are NOT $S$. 2. "No $S$ is $N$" means there is no overlap between $S$ and $N$. Conclusions Check: I. "All Neural Networks can be Synapses" - False. Because "Only a few" implies some $NN$ are definitely NOT $S$. II. "Some Neural Networks are not Neurons" - True. The part of $NN$ that is $S$ can never be $N$ (since no $S$ is $N$). Therefore, only II follows.

Question 2

2. Analyze the logical consistency of the following conclusions.

A) Both conclusion I and II follow

B) Only conclusion II follows

C) Only conclusion I follows

D) Neither I nor II follows

Answer

Correct Answer: B

Solution: 1. "Only Quantum Bits ($QB$) are Superpositions ($S$)" is equivalent to "All $S$ are $QB$" AND "$S$ cannot belong to any other category except $QB$". 2. "Some $QB$ are not Entanglements ($E$)" allows for $QB$ to partially overlap with $E$. Conclusions Check: I. "Some Superpositions are Entanglements" - False. Because of the "Only" condition, $S$ can only be $QB$ and nothing else. II. "No Entanglement is a Superposition" - True. Following the same logic, since $S$ is exclusively $QB$, it cannot be $E$. Therefore, only II follows.

Question 3

3. Evaluate the following syllogism based on ancient artifacts.

A) Only conclusion I follows

B) Only conclusion II follows

C) Both conclusion I and II follow

D) Neither I nor II follows

Answer

Correct Answer: C

Solution: 1. All $M \subset S$ 2. $S \cap P \neq \emptyset$ 3. $P \cap D = \emptyset$ Conclusions Check: I. "All Scrolls can never be Digital" - True. Since some Scrolls are Papyrus and no Papyrus is Digital, that specific portion of Scrolls can never be Digital. II. "Some Manuscripts being Digital is a possibility" - True. There is no direct or indirect restriction preventing $M$ from overlapping with $D$. Both follow.

Question 4

4. Evaluate the security logic.

A) Only conclusion I follows

B) Only conclusion II follows

C) Both follow

D) Neither follows

Answer

Correct Answer: B

Solution: 1. "Only a few $F$ are $E$" (Some $F$ are $E$ and Some $F$ are not $E$); "All $F$ being $E$" is impossible. 2. "Only a few $E$ are $D$" (Some $E$ are $D$ and Some $E$ are not $D$). 3. No $D$ is $V$. Conclusions Check: I. "All Firewalls can be Encryptions" - False (Violates "Only a few"). II. "Some Encryptions can be Viruses" - True. While no $D$ is $V$, there is no restriction on the part of $E$ that is NOT $D$ being $V$. Only II follows.

Question 5

5. Astronomical Reasoning.

A) Only conclusion I follows

B) Only conclusion II follows

C) Both conclusion I and II follow

D) Neither follows

Answer

Correct Answer: C

Solution: 1. $70\%$ $N$ are $S$ is equivalent to "Some $N$ are $S$". 2. All $S$ are $P$. 3. "Only a few $P$ are $BH$". Conclusions Check: I. "Some Nebulas are Pulsars" - True. Since some $N$ are $S$ and all $S$ are $P$, the intersection is guaranteed. II. "All Pulsars being Nebulas is a possibility" - True. There's no "Only a few" restriction between $P$ and $N$ that prevents $P$ from being entirely inside $N$. Both follow.

Question 6

6. Physics Logic.

A) Both conclusion I and II follow

B) Only conclusion II follows

C) Only conclusion I follows

D) Neither follows

Answer

Correct Answer: A

Solution: 1. $P \subset A$ 2. $A \subset M$ 3. $M \cap Q = \emptyset$ Conclusions Check: I. "Some Quarks are not Protons" - True. Since no $M$ is $Q$, and $P$ is inside $M$, then no $P$ is $Q$. If no $P$ is $Q$, then all $Q$ are not $P$. II. "No Proton is a Quark" - True. As $P \subset M$ and $M$ has no overlap with $Q$. Both follow.

Question 7

7. Agricultural Logic.

A) Only conclusion I follows

B) Only conclusion II follows

C) Either I or II follows

D) Neither follows

Answer

Correct Answer: B

Solution: 1. "Only a few $G$ are $C$" (Some $G$ are $C$, Some $G$ are not $C$). 2. $C \cap L = \emptyset$. 3. $L \cap P \neq \emptyset$. Conclusions Check: I. "All Grains can be Cereals" - False (Due to "Only a few"). II. "Some Pulses are not Cereals" - True. The part of $P$ that is $L$ can never be $C$ because no $C$ is $L$. Only II follows.

Question 8

8. Geology Logic (Either-Or possibility check).

A) Only conclusion I follows

B) Only conclusion II follows

C) Either I or II follows

D) Both follow

Answer

Correct Answer: B

Solution: 1. $M \cap L \neq \emptyset$. 2. $L \cap B = \emptyset$. Conclusions Check: I. "All Magma can be Basalt" - False. The part of $M$ that is $L$ can never be $B$. II. "Some Magma are not Basalt" - True. The part of $M$ that is $L$ is definitely not $B$. Only II follows.

Question 9

9. Atmospheric Logic.

A) Only conclusion I follows

B) Only conclusion II follows

C) Both follow

D) Neither follows

Answer

Correct Answer: D

Solution: 1. "Only $O$ is $B$" means All $B$ are $O$, and $B$ cannot be anything else (specifically, $B$ cannot be $Oz$). 2. Some $O$ are $Oz$. Conclusions Check: I. "All Ozone being Breathable is a possibility" - False. If all $Oz$ were $B$, then $B$ would be something other than just $O$. The exclusivity rule of "Only" prohibits this. II. "Some Breathable can be Ozone" - False. $B$ is exclusively $O$. It cannot overlap with any other separate category like $Oz$. Neither follows.

Question 10

10. Mathematical Logic.

A) Only conclusion I follows

B) Only conclusion II follows

C) Both follow

D) Neither follows

Answer

Correct Answer: A

Solution: 1. $V \subset T$ 2. $T \cap S = \emptyset$ 3. "Only a few $S$ are $M$" 4. $M \cap C \neq \emptyset$ Conclusions Check: I. "No Vector is a Scalar" - True. Since $V$ is entirely inside $T$ and $T$ has no overlap with $S$. II. "All Matrices can be Tensors" - False. Some $M$ are $S$ (from "Only a few $S$ are $M$"). Since no $S$ is $T$, that part of $M$ which is $S$ can never be $T$. Only I follows.

Competitive Exams : Reasoning Ability - Syllogism (Set 1) | Concept of Maths