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Are triflate, tosylate and mesylate the only good leaving groups?
No. They are the best , but there are other good leaving groups.
Triflate, tosylate, and mesylate ions are excellent leaving groups, because the sulfonate ions can stabilize the negative charge via resonance.
Good leaving groups are weak bases. These ions are weak bases because they are the conjugate bases of very strong sulfonic acids.
But the halide ions Cl⁻, Br⁻, and I⁻ are also good leaving groups. They are the conjugate bases of the strong acids HCl, HBr, and HI.
Water is another good leaving group. It is the conjugate base of the strong acid H₃O⁺.
Here's a video on what makes a good leaving group.