Let us also assume that the world population forms the Universal Set. For the sake of simplicity, we assume that these three are the only religions in the world. However, we know that there are people in this world who do not believe in any of these three.
We also know that the sets of believers of all religions are mutually exclusive, just as your race is. Therefore it is not possible to have a believer in two or more religions. Thus we have:
It is known that any major religion believes it is the only true religion, and that all other religions are false. Therefore, assuming red represents false religions, and green represents true religions, the diagram would look like this to a believer in religion A:
This can easily be changed to a believer in religion B, where the set of believers of religion B would be green, and the set of believers in religion A would be red. How do we now conclude which is the actual true religion? If you take only the green colours and do an “Union” operation, all religions are true. If you do an “Intersection” operation, no religion is true. If you take all the reds and do a “Union” operation, all religions are false.
Also, it is interesting to note that in the above example, one religion is confirmed twice to be false, compared to the one time it confirms itself to be true. In the real world, a religion is confirmed to be false, as many number of times as the number of other religions claiming themselves to be the only true religion. Therefore any given religion is confirmed to be false several times, while it only confirms itself once to be true.
Now, it is a common knowledge that the believers of religion A believes that anyone who does not believe in religion A goes to hell. Let us assume that heaven and hell exist. If you take the colour of the set of people going to hell according to religion A as golden yellow, we have:
We can easily change the above diagram to represent the view held by believers of religion B. Their set would become white, while the set of religion A would become golden yellow.
If you do a “union” operation on these three diagrams, the entire population of the earth is going to hell. If you do an “intersection” operation, anyone who does not believe in a religion that would take them to heaven, would essentially go to hell. It doesn’t matter which religion he chooses, as long as it will take him to heaven.
Conclusions: Thus we see that we cannot determine with absolute confidence that any of the world religions could be the true religion, but at the same time, we cannot conclude that all religions are false.
Also, to go to heaven, we must choose a religion that most appeases us, as a person who rejects all religions would go to hell. This means that we are essentially given the freedom of faith – to choose the religion we want to believe. This also means that we can create our own private religion as well, as the only requirement to go to heaven is that you believe in a religion that takes you to heaven. Your own private religion can also take you to heaven if you want it to!
The third conclusion is that, we cannot be absolutely sure that we would go to heaven even if we believe in a religion. If God chooses to do an “union” operation on all the religions, we are doomed to hell. Let us hope that He does an “intersection” instead.