Syllogism

- This chapter deals with venn diagrams used to solve statements to form conclusions. So, the questions will be basically of statement-conclusion type.
- In some questions we might be asked to draw an inference out of the given information.
- To understand this better, we follow some types of statements:

__Statement 1 ➡️ All A are B__

- This phrase means that A is contained in B but not necessarily vice versa. This means A is a subset of B, but B may not be a subset of A. The Venn diagram for this is:

- In this diagram, it is visible that circle A is inside the circle B, which means that B contains the entire A, i.e. All A are B.

__Statement 2 ➡️ A = B__- In this case, the conclusion is similar to the first type, i.e. “All A are B”. Here not only “All A are B”, but also “All B are A”. This means A is a subset of B and B is also a subset of A. The Venn diagram is:

- Here A is contained in B and so is B contained in A. So, here A contains all B and again B also contains all A.

__Statement 3 ➡️ No A are B__- It is simply understandable that B does not contain any of A and so A is not contained in B. This means that A and B are disjoint sets. The Venn diagram for this case is:
- Here no part of A is present inside of B and similarly, no part of A is present in A. So neither A nor B contain any part of B or A respectively.

__Statement 4 ➡️ Some A are B__- This is the case when some of A is in B that is A and B are intersecting, and thus some B are A will also be true. The Venn diagram depiction is as:
- Here, the shaded portion indicates that some portion of A is contained in B while the unshaded portion is uncertain portion and does not indicate anything whether A is contained in B or not.

__Statement 5 ➡️ Some A are not B__- This means that some portion of A is not included in B for sure while the other part of A is uncertain whether it is included in B or not. The Venn diagram is;
- In this, some portion of A is surely not included in B while there is no surety whether the shaded region is included in B or not.