Question: In our road we have a crab apple tree that has fruits but there have never been any small new trees rooting from the crab apples. Once, years ago, there were 3 crab apple trees within 100 yards but 2 of these were destroyed by some ignorant house owners. However in my 83 years of living within 50 yards of these three trees I have never seen any young new seedling trees. Some of the apples must have fallen onto the surrounding soil that is never disturbed. Will an apple tree grow if I deliberately plant some of the fruit from this one remaining tree?

Answer: 
Not if you just plant a whole fruit, no, very unlikely. There is a way to do it, but you need to extract the seeds from the fruit in autumn by cutting it open, lifting the seeds out carefully, then removing any remaining pulp by flushing with water. After drying, they need cold stratification for up to 120 days - a description of how to do all this is shown here <http://homeguides.sfgate.com/propagating-crabapple-seeds-27860.html>, but you should bear in mind that Malus varieties do not come true from seed. The named varieties you buy are vegetatively propagated to ensure they are the right variety - from seed, you don't know what you'll get, other than it'll be a crabapple of some sort.
If you think about the reason why fruit exist, it is to employ animals to disperse the seeds far away from the parent tree. So if this works (which we can assume it does based on the principles of evolution) one might expect that not many of the seeds will remain near the parent for the requisite amount of time (the cold of winter, the warm of spring) to induce germination. Those seeds that are dropped relatively nearby will face a lot of competition: shading from other plants, predation, gardening activities of humans, etc.

The previous comment about apples not coming true to seed is valid, except what this usually means is that cultivars of apple result in something more like crab apples, which is not a problem in your case. If you plant a bunch of seeds and keep them the cold over the winter, you should get some saplings in the following year.