Incorrect Statement: For a given water content, big size aggregate gives less workability.

Explanation:
Workability refers to the ease with which concrete can be mixed, transported, placed, and compacted without segregation or excessive bleeding. It is an important property of concrete that affects its handling and performance. Workability is influenced by various factors, including water-cement ratio, aggregate size and shape, and the use of admixtures.

Water-Cement Ratio:
- The water-cement ratio is the ratio of the weight of water to the weight of cement in a concrete mix.
- Workability generally increases with an increase in the water-cement ratio. This is because a higher amount of water provides more lubrication and makes the mix more fluid, allowing for easier placement and compaction.
- However, excessively high water-cement ratios can result in a decrease in the strength and durability of the concrete.

Aggregate Size:
- The size of the aggregates used in concrete can affect its workability.
- Smaller size aggregates have a larger surface area, leading to higher water demand and reduced workability.
- On the other hand, bigger size aggregates have a lower surface area, requiring less water and resulting in increased workability.
- Therefore, the statement that big size aggregate gives less workability is incorrect.

Lean Concrete:
- Lean concrete refers to a concrete mix with a low cement content and a high water-cement ratio.
- In lean concrete, the workability is reduced because of the high water-cement ratio and the absence of sufficient cementitious material to provide cohesiveness.
- The mix becomes more fluid, which makes it difficult to handle and place.

Air Entrained Concrete:
- Air entrained concrete is a type of concrete that contains microscopic air bubbles distributed uniformly throughout the mix.
- The inclusion of air entraining admixtures improves the workability of concrete by increasing its cohesiveness and reducing the amount of water required.
- The air bubbles act as lubricants, making the mix more flowable and easier to handle.

In conclusion, the incorrect statement is option B, which states that for a given water content, big size aggregate gives less workability. In reality, big size aggregates provide increased workability due to their lower surface area, requiring less water for a given water content.