Friction on tyres The force of friction is directly proportional to area of contact. But then why do the tyres of trucks and other large vehicles have big gaps in them? It reduces the area of contact so frictional force should be else. But by observation it is seen that it provides more friction. Can you please explain the reason for it?
 A: 
The force of friction is directly proportional to area of contact.

This is largely counteracted by the reduction of the normal force per unit area with a larger area of contact. Taking this to the extreme yields the physics 101 assumption that area of contact plays no role in the frictional force. Strictly speaking, this is of course incorrect. It's physics 101, after all.
One need only to look at cars built for competitive racing to see that this is indeed incorrect. The designers of those cars go out of their way to shed all excess weight. Race cars would use the skinniest (and lightest) tires possible if surface area didn't matter. Race cars from 100 years ago did indeed use the skinniest of tires. Developers of race cars quickly found that tire size does matter. The relationship however is nowhere near linear.

But then why do the tyres of trucks and other large vehicles have big gaps in them?

If you know the road will be perfectly dry, the best tire to use would be a slick. What if the road isn't perfectly dry? Slicks and wet roads are a dangerous combination. With slicks, the coefficient of friction can be over 0.9 on dry pavement but less than 0.1 on a wet road. Tires intended for everyday use have grooves. These grooves do two things. One is that they give the water somewhere to go so that there is some water-free contact between tire and road. The other is that they channel water away from the tire. While those grooves do hinder friction on perfectly dry pavement, they drastically improve performance (compared to slicks or skinny tires) on wet pavement.

Reference: Personal. The tires on my car are 295/35ZR18 99Y (rear), 275/40ZR17 98Y (front). That means if I was foolish enough to desire to do so, I could drive in excess of 300 kph on dry pavement without worrying that the tires might melt (and my car supposedly can do that and more). Wet pavement is a different beast. My car has a desire to go sideways on wet roads -- and I don't have slicks.
A: "It reduces the area of contact so frictional force should be else."
It is important to note that the area of contact does not at all change the friction that you experience. You can work out the equations and see that kinetic friction only depends on the material and mass of the object when on earth. Basically something with smaller area will have more force in that small area, counteracting the effect. 
Grooves on tires prevent hydroplaning.
A: "The force of friction is directly proportional to area" and also
to the downward presure over that area.
For a car or truck, with flexible tires, the tire gage tells you the
tires' (circa 30 psi) internal pressure, and the 'area of contact' is
just the weight of the vehicle, divided by that tire pressure.
No matter how the tires are arranged or patterned, the downward pressure
times contact area is the weight of the vehicle.  The pattern
is intended to break the lubricating film of water when roads
are wet.
So, big trucks can pull more, because they weigh more (put more weight over
the driving wheels).
A: For the case of tires on a road, the surface area is unimportant. Here's why.
The frictional force is proportional to the normal force, the force pressing the two surfaces together. Let's compare a slick, tire A, with no treads at all to a treaded tire, tire B. Suppose B has only half the surface area of A. Either tire on a given car will experience the same overall force pressing it into the road, the weight of the car over that contact point. In the case of tire A there is twice as much area over which to spread that force so the force on any given unit of area is only half as much as the force on a unit area of tire B. Tire B has only half the contact area of tire A but each unit of area has to support twice the force. Twice the force per area x half the overall area = same overall normal force contributing to friction.
The purpose of treads in tires is to provide a place for the contact surface in which to press the water, avoiding a lubricating layer sandwiched between tire and road.
The puropse of slicks, according to Paul Hewitt, Conceptual Physics, is to provite a large surface area with which to dissipate heat from rapid accelerations.
