Question

Choose the set of three statements where the third statement can be logically derived from the preceding two.
Statements:
1. All human beings need education.
2. All teachers need training.
3. Education is provided by the teachers.
4. X is a teacher.
5. X needs training.
6. Students are future of a nation.
The set of statements is:

• A. 1, 2, 5
• B. 2, 3, 4
• C. 2, 4, 5
• D. 4, 5, 6

Answer 1

The Correct Option is C

The correct option is (C): 2, 4, 5.

Answer 2

This question mixes a general categorical statement with a statement about a specific individual, X. Let's check each option:

1. 1, 2, 5: 'All human beings need education' and 'All teachers need training' are both general statements about categories, but neither mentions X specifically, so neither can support a conclusion about X needing training.
2. 2, 3, 4: 'All teachers need training' and 'Education is provided by the teachers' both discuss teachers in general, but combining them does not produce 'X is a teacher', since neither premise says anything about who X is.
3. 2, 4, 5: 'All teachers need training', a general rule covering every teacher, combined with 'X is a teacher', a specific fact placing X inside that category, directly forces the conclusion that X, being a teacher, needs training, exactly statement 5.
4. 4, 5, 6: 'X is a teacher' and 'X needs training' both concern X, but the proposed conclusion, 'Students are future of a nation', introduces students, a term absent from both premises.

Only applying the general rule that all teachers need training to the specific fact that X is a teacher logically forces the conclusion that X needs training.

Therefore, the correct answer is 2, 4, 5.

Answer 3

Think of a group of all Teachers (T), all of whom fall inside the group that Needs training (N), as stated in statement 2. Statement 4 places a specific individual, X, inside the Teachers circle. Let's check each option using this picture:

1. 1, 2, 5: Statement 1 concerns all human beings needing education, and statement 2 concerns all teachers needing training, two separate universal groups with no individual X mentioned in either, so no conclusion about a specific person X follows.
2. 2, 3, 4: Statement 2 nests Teachers inside Needs-training, and statement 3 says teachers provide education, a different circle entirely from where X is placed, these do not combine to place X inside the Teachers circle.
3. 2, 4, 5: Statement 2 nests the entire Teachers circle inside Needs-training, and statement 4 places X specifically inside the Teachers circle. Since X sits inside Teachers, and Teachers sits entirely inside Needs-training, X must also sit inside Needs-training, exactly statement 5.
4. 4, 5, 6: Statement 4 places X inside Teachers and statement 5 places X inside Needs-training, both about X specifically, but the offered conclusion, statement 6, shifts entirely to a different group, students, never mentioned in either premise.

Placing X inside the Teachers circle and then placing that whole circle inside the Needs-training circle is the only chain here that correctly forces X into the Needs-training group, giving statement 5.

Therefore, the correct answer is 2, 4, 5.