# Logical Reasoning - Logical Deduction

*Directions to Solve*

In each of the questions below are given three statements followed by three conclusions numbered I, II and III, You have to take the given statements to be true even if they seem to be at variance from the commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

**Statements: ** Some pens are books. All schools are books. Some colleges are schools.

**Conclusions:**

- Some colleges are pens.
- Some pens are schools.
- Some colleges are books.

Some pens are books. All schools are books.

Since the middle term 'books' is not distributed even once in the premises, so no definite conclusion follows.

Some colleges are schools. All schools are books.

Since one premise is particular, the conclusion must be particular and should not contain the middle term.

So, it follows that 'Some colleges are books'. Thus, III follows.

Some pens are books. Some colleges are books.

Since both the premises are particular, no definite conclusion can be drawn.

Hence, only III follows.

**Statements: ** All trains are buses. No room is bus. All boats are rooms.

**Conclusions:**

- No boat is train.
- No bus is boat.
- No train is room.

All trains are buses. No room is bus.

Since both the premises are universal and one premise is negative, the conclusion must be universal negative (E-type) and should not contain the middle term. So, it follows that 'No train is room'. Thus, III follows.

All boats are rooms. No room is bus.

As discussed above, it follows that 'No boat is bus'.

II is the converse of this conclusion and so it holds. All trains are buses. No boat is bus.

Again, it follows that 'No train is boat'. I is the converse of this conclusion and so it holds.

**Statements: ** Some mountains are hillocks. Some mountains are rivers. Some mountains are valleys.

**Conclusions:**

- All mountains are either hillocks or rivers or valleys.
- No valley is river.
- Some river are valleys.

Since each combination of premises shall contain two particular premises, no definite conclusion can be drawn. However, II and III are statements involving the extreme terms of the last two premises and form a complementary pair. Thus, either II or III follows.

**Statements: ** Some blades are hammers. Some hammers are knives. Some knives are axes.

**Conclusions:**

- Some axes are hammers.
- Some knives are blades.
- Some axes are blades.

Since each combination of premises has two particular premises, so no definite conclusion follows.

**Statements: ** Some boxes are hammers. Some hammers are beads. All beads are rings.

**Conclusions:**

- Some rings are hammers.
- Some hammers are boxes.
- Some rings are boxes.

II is the converse of first premise and so it holds.

Some boxes are hammers. Some hammers are beads.

Since both the premises are particular, no definite conclusion can be drawn.

Some hammers are beads. All beads are rings.

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some hammers are rings'. I is the converse of this conclusion and so it holds.

Some boxes are hammers. Some hammers are rings.

Since both the premises are particular, no definite conclusion can be drawn.