Statements & Conclusions Concepts

1. Direct Conclusions

What It Means

A conclusion follows only if it must be true based on the given statements.

❌ Do not use outside knowledge.

✅ Use only the information provided.

Quick Rule

Statements
     │
     ▼
Logical Check
     │
     ▼
Must be True?
     │
  Yes ───► Follows ✅
     │
   No ───► Does NOT Follow ❌

---

Example

Statements

• All birds have feathers.
• A swan is a bird.

Question

Does the conclusion “A swan has feathers” follow?

Solution

Visualize the sets:

+-----------------------+
|        Birds          |
|                       |
|  +---------------+    |
|  |    Swans      |    |
|  +---------------+    |
|                       |
| (All birds have       |
|  feathers)            |
+-----------------------+

Since:

• Every bird has feathers.
• Swan is a bird.

Therefore,

Swan
 ↓
Bird
 ↓
Has feathers

Answer

✅ Yes, the conclusion follows.

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2. Don’t Add Extra Information

What It Means

Many questions try to make you assume facts that were never stated.

Only use the given statement.

Example

Statement

The school closes if it rains heavily.

Conclusion

The school was closed yesterday.

Solution

The statement only says:

Heavy Rain
     │
     ▼
School Closed

But we don’t know whether it rained yesterday.

The school may also close because of:

Holiday
Strike
Power Failure
Festival
Election

Nothing tells us which happened.

Answer

❌ Does NOT follow.

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3. Conditional Statements (If…Then)

Basic Rule

If P → Q

Example:

If you pay the fee
        │
        ▼
You receive a receipt

Valid Logic

Pay Fee
   │
   ▼
Receipt

Also valid:

No Receipt
     │
     ▼
No Payment

(Contrapositive)

Invalid Logic

Didn't Pay
     │
     ▼
No Receipt

This is not guaranteed.

Someone may receive a receipt because of:

• refund
• scholarship
• exemption

---

Example

Statement

If you pay the fee, you get a receipt.

Conclusion A

If you did not get a receipt, you did not pay.

Receipt?
   No
    │
    ▼
Payment?
   No

✅ Valid

---

Conclusion B

If you did not pay, you did not get a receipt.

Didn't Pay
      │
      ▼
No Receipt

Not always true.

Answer

• ✅ Conclusion A follows.
• ❌ Conclusion B does not.

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4. Multiple Statements

Sometimes several statements are connected.

Connect them one by one.

Example

Statements

• All engineers are logical.
• Some logical people play chess.

Diagram

          Logical People
+----------------------------------+
|                                  |
|  +-------------+                 |
|  | Engineers   |                 |
|  +-------------+                 |
|                                  |
|        (Some overlap)            |
|        +-------------+           |
|        |Chess Players|           |
|        +-------------+           |
|                                  |
+----------------------------------+

Notice:

The chess players may be outside the engineer group.

Possible arrangement:

Logical People

+-------------------------------------------+

  Engineers

  +---------+

  |         |

  +---------+



                     Chess Players

                     +---------+

                     |         |

                     +---------+

+-------------------------------------------+

Nothing says the two groups overlap.

Question

Does

Some engineers are chess players

follow?

Answer

❌ No.

The chess players could be different logical people.

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Common Patterns

Universal Statement

All A are B

A
│
▼
B

---

Chain Rule

All A are B
All B are C

A
│
▼
B
│
▼
C

Therefore

All A are C ✅

---

”Some”

Some A are B

 A
╲ ╱
 X
╱ ╲
 B

Never assume:

• All A are B ❌
• Some B are A always gives more information ❌

Only the overlap is guaranteed.

---

”No”

No A are B

A      B

(O)    (O)

No overlap.

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Tips

• Read exactly what is written.
• Never use real-world knowledge.
• “Some” means at least one, not all.
• “All” creates a complete subset.
• Conditional statements (If P → Q) do not mean If not P → not Q.
• A conclusion follows only if every valid diagram makes it true. Otherwise, it does not follow.