Reasoning

Correct answer: C

I is incorrect: Exactly one of P and Q is selected. P is selected. → Q is not selected. Exactly one excludes simultaneous selection. II is correct: Every completed form has a signature. This form has no signature. → This form is not completed. The necessary condition for completion is absent.

Correct answer: B

The electric buses belong to the non-diesel category in the stated setting.

Correct answer: A

I is correct: If a card is valid, a gate opens. The gate opened. → Card validity cannot be concluded from this alone. Other conditions could also open the gate; affirming the consequent is invalid. II is incorrect: All keys in drawer A open lock L. Key K is in drawer A. → Key K opens lock L. K falls under the universal rule.

Correct answer: B

I is incorrect: If it rains, play stops. Play continued without stopping. → It did not rain during that play. The stated conditional rules out rain when its consequence is absent. II is correct: Either both doors are locked or neither is locked. The first is locked. → The second door is locked. The doors must have matching lock states.

Correct answer: C

The inspectors who are listed engineers cannot be absent.

Correct answer: B

I is correct: If a card is valid, a gate opens. The gate opened. → Card validity cannot be concluded from this alone. Other conditions could also open the gate; affirming the consequent is invalid. II is incorrect: Only registered members may enter. Ravi entered in compliance with the rule. → Ravi is registered. Registration is a necessary condition for permitted entry.

Correct answer: C

I is incorrect: No square in a diagram is blue. Some circles in the diagram are blue. → Some blue shapes are not squares. The stated blue circles cannot be squares under the premise. II is correct: All certified trainees passed. Mina did not pass. → Mina is not a certified trainee. Failure to pass excludes membership in the certified group.

Correct answer: B

The necessary condition for completion is absent.

Correct answer: A

I is incorrect: Either both doors are locked or neither is locked. The first is locked. → The second door is locked. The doors must have matching lock states. II is correct: All archived files are indexed. Some letters are archived files. → Some letters are indexed. The archived letters fall within the indexed class.

Correct answer: C

The stated conditional rules out rain when its consequence is absent.

Correct answer: D

I is incorrect: If a switch is on, a lamp glows. The lamp does not glow. → The switch is not on. This is the valid contrapositive of the conditional. II is correct: No poets in a club are accountants. Some members are poets. → Some members are not accountants. The stated poets supply the required non-accountant members.

Correct answer: B

K falls under the universal rule.

Correct answer: D

I is correct: At least one of A and B attends. A does not attend. → B attends. The inclusive disjunction requires B when A is absent. II is correct: Some buses here are electric. No electric vehicle here uses diesel. → Some buses here do not use diesel. The electric buses belong to the non-diesel category in the stated setting.

Correct answer: A

The doors must have matching lock states.

Correct answer: C

I is incorrect: If it rains, play stops. Play continued without stopping. → It did not rain during that play. The stated conditional rules out rain when its consequence is absent. II is incorrect: Every completed form has a signature. This form has no signature. → This form is not completed. The necessary condition for completion is absent.

Correct answer: A

Other conditions could also open the gate; affirming the consequent is invalid.

Correct answer: C

I is correct: If a switch is on, a lamp glows. The lamp does not glow. → The switch is not on. This is the valid contrapositive of the conditional. II is correct: All roses in a box are red. This flower is a rose in that box. → This flower is red. The universal statement applies to the specified rose.

Correct answer: B

The stated blue circles cannot be squares under the premise.

Correct answer: B

I is correct: Only registered members may enter. Ravi entered in compliance with the rule. → Ravi is registered. Registration is a necessary condition for permitted entry. II is correct: Some buses here are electric. No electric vehicle here uses diesel. → Some buses here do not use diesel. The electric buses belong to the non-diesel category in the stated setting.

Correct answer: D

Failure to pass excludes membership in the certified group.

Correct answer: B

I is correct: If a card is valid, a gate opens. The gate opened. → Card validity cannot be concluded from this alone. Other conditions could also open the gate; affirming the consequent is invalid. II is incorrect: Every completed form has a signature. This form has no signature. → This form is not completed. The necessary condition for completion is absent.

Correct answer: D

The universal statement applies to the specified rose.

Correct answer: C

I is incorrect: No metal token is flexible. This token is flexible. → This token is not a metal token. A flexible token cannot belong to the excluded class. II is incorrect: If a switch is on, a lamp glows. The lamp does not glow. → The switch is not on. This is the valid contrapositive of the conditional.

Correct answer: B

The stated poets supply the required non-accountant members.

Correct answer: C

I is correct: Some buses here are electric. No electric vehicle here uses diesel. → Some buses here do not use diesel. The electric buses belong to the non-diesel category in the stated setting. II is correct: All archived files are indexed. Some letters are archived files. → Some letters are indexed. The archived letters fall within the indexed class.