Can one use "since" and "that's why" in one sentence?

Question

Is the following sentence gramatically correct? If 'no',please, give your reasons.

• Since these two photos illustrate two different types of exercising that’s why I think they are good for our project.

The whole passage:

• In the first photo you can see young people playing volleyball outdoors. In the second picture there is a young woman running on a treadmill in the gym. Even though they seem to be related to the topic of exercising they show different aspects of it. In the first photo there is a volleyball game which is a team sport and the second picture conveys the concept of exercising alone. Since these two photos illustrate two different types of exercising that’s why I think they are good for our project.

Answer 1

This sentence is (probably) grammatically correct, strictly speaking. But it's not semantically correct.

Firstly, the "Since" and "that's why" are redundant. Secondly, "Since...exercising" is a dependent clause. Therefore, the "that's" cannot refer to it but rather must refer to the preceding: In the first photo there is a volleyball game which is a team sport and the second picture conveys the concept of exercising alone. So if we interpret the passage literally, the meaning is dramatically changed from what is probably intended.

One might say:

Since these two photos illustrate two different types of exercising, I think they are good for our project.

Or one might say any of the following:

These two photos illustrate two different types of exercising; that’s why I think they are good for our project.

These two photos illustrate two different types of exercising. That’s why I think they are good for our project.

These two photos illustrate two different types of exercising and that’s why I think they are good for our project.

But one shouldn't use the original sentence in writing. In casual speaking, it might be more acceptable, or even preferable, to use this phrasing: it helps to emphasize the cause-and-effect, even if technically incorrect.