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Here, I've done Alternate Gates of all Gates that we have in Alternative Gates. For proving it, I need to get 1 in each and every gate for glowing LED light by giving same inputs in original and alternative gates.

In these alternative gates, 

1. The NOR gate is an alternative gate to the AND gate, when we give NOT gate to both two inputs. Here, in input, I've given 1 to both inputs. So, in both the AND gate and the alternative gate, output is succeeded in glowing the light.
2. The OR gate is an alternative gate to the NAND gate, when we give NOT gate to both two inputs. Here, in input, I've given 0 to both inputs. So, in both the NAND gate and the alternative gate, output is succeeded in glowing the light.
3. The NAND gate is an alternative gate to the OR gate, when we give NOT gate to both two inputs. Here, in input, I've given 1 to both inputs. So, in both the OR gate and the alternative gate, output is succeeded in glowing light.
4. The AND gate is an alternative gate to the NOR gate, when we give NOT gate to both two input. Here, in input, I've given 0 to both the inputs. So, in both the NOR and the alternative gate, output is succeeded in glowing light. 
5. Ex-NOR gate is an alternative gate to the Ex-OR gate, when we give NOT gate to any one of the input. Here, in input, I've given 1 as 1st input and 0 as the second input to get output as 1. So, in both the Ex-OR and alternative gates are succeeded in glowing the light.
6. Ex-OR gate is an alternative gate to the Ex-NOR gate, when we give NOT  gate to any one of the input. Here, in input, I've given 0 to both the inputs. So, in both the Ex-NOR and alternative gates are succeeded in glowing the light.