Syllogism for Banking - SSC Exams

Directions (Q. 1-5): In each of the questions below are given four statements followed by four conclusions numbered I, II, III and IV. You have to assume everything in the statements to be true even if they seem to be at variance with commonly known facts and then decide which of the four given conclusions logically follows from the statements, disregarding commonly known facts, and select the appropriate answer.

1. Statements: Some numbers are digits.

                                 All digits are alphabets.

                                 No alphabet is a vowel.

                                 All consonants are vowels.

Conclusions:

I.    No digit is a vowel.

II.  No alphabet is a consonant.

III.  No vowel is a number.

IV.  All vowels are numbers.

        1) Only I and III follow                           

        2) Only II and IV follow

        3) Only I and II follow

        4) Only I, II and III follow

        5) Only I , II and either III or IV follow

2. Statements: All documents are files.

                                 Some files are papers.

                                 All papers are certificates.

                                 No certificate is a manuscript.

Conclusions:

I.    At least some documents are papers.

II.  No manuscript is a document.

III. At least some certificates are files.

IV.  No paper is a document.

        1) Only I , II and IV follow        2) Only II and III follow

        3) Only I and IV follow      4) Only III follows

        5) None of these

3. Statements: No group is people.

                                 All people are animals.

                                 All animals are plants.

                                 All plants are roots.

Conclusions:

I.    No group is a plant.

II.  All people are plants.

III.  At least some groups are plants.

IV.  All plants are groups.

        1) Only II follows

        2) Only I and IV follow

        3) Only II and III follow

        4) Only III and IV follow

        5) None of these

4. Statements: Some jobs are vacancies.

                                 All jobs are works.

                                 No work is a trade.

                                 All professions are trades.

Conclusions:

I. At least some works are jobs.

II.  No vacancy is a trade.

III.  No profession is a work.

IV.  At least some works are professions.

        1) All I, II, III and IV follow

        2) Only II, III and IV follow

        3) Only I and IV follow

        4) None follows

        5) Only I and III follow

5. Statements: All marks are grades.

                                 No grade is a score.

                                 All letters are scores.

                                 All scores are characters.

Conclusions:

I.   At least some letters are grades.

II. At least some scores are grades.

 III.   At least some characters are marks.

IV. Some characters are letters.

        1) Only II and IV follow

        2) Only IV follows

        3) Only I and III follow

        4) All I, II, III and IV follow

        5) None follows

Answers:

1. 3; All digits are alphabets (A) + No alphabet is a vowel (E) = A + E = E = No digit is a vowel. Hence, conclusion I follows.

1. No alphabet is a vowel → conversion→ No vowel is an alphabet. Now, All consonants are vowels (A) + No vowel is an alphabet (E) = A + E = E = No consononant is an alphabet (E) → conversion → No alphabet is a consonant. Hence, conclusion II follows.
   Again, Some numbers are digits + All digits are alphabets = I + A = I = Some numbers are alphabets (I) + No alphabet is a vowel (E) = I + E = O = Some numbers are not vowels. Hence, conclusion III and IV do not follow.

2. 5; All documents are files (A) + Some files are papers (I) = A + I = No conclusion. Hence, conclusion I, II and IV do not follow. However, I and conversion of IV make a complementary pair. Hence, either I or IV follows. Again Some files are papers (I) + All papers are certificates (A) = I + A = I = Some files are certificates → conversion → Some certificates are files. Hence, conclusion III follows.

3. 5; All people are animals (A) + All animals are plants (A) = A + A = A = All people are plants. Hence, conclusion II follows. Now, No group is people (E) + All people are plants (A) = E + A = O* = Some plants are not groups. Thus, conclusion I, III and IV do not follow. However, I and III make a complementary E-I pair. Hence, either I or III follows.

4. 5; All jobs are works → implication → Some works are jobs. Hence, conclusion I follows.

1. Again, Some jobs are vacancies → conversion → Some vacancies are jobs + All jobs are works (A) = I + A = I = Some vacancies are works (I) + No work is a trade (E) = I + E = O = Some vacancies are not trades. Hence, conclusion II does not follow. Now, No work is a trade → No trade is a work
   Again, All professions are trades (A) + No trade is a work (E) = A + E = E = No profession is a work. Hence, conclusion III follows. But conclusion IV does not follow.

5. 2; No grade is a score → conversion → No score is a grade. Now, All letters are scores (A) + No score is a grade (E) = A + E = E = No letter is a grade. Hence, conclusion I does not follow. And conclusion II does not follow from statement II.

1. Again, All marks are grades (A) + No grade is a score (E) = A + E + E = No mark is a score (E) + All scores are characters (A) = E + A = O* = Some characters are not marks. Hence, conclusion III does not follow. But All letters are scores (A) + All scores are characters (A) = A + A = A = All letters are characters → conversion → Some characters are letters. Hence, conclusion IV follows.