Law of Syllogism states that if A is equal to B and B is equal to C, then A must be equal to C.
Here, lets say - If the sun is shining be 'A' , then it is a beautiful day be 'B' and then we will go for a bike ride be 'C'
Then according to the stated law, A equals B and B equals C, thus equaling A and C.
This argument does not follow the Law of Syllogism, because the hypothesis "If we go for a bike ride" is matched by the statement "then it is a beautiful day." This conclusion is based on the premisse: "If it is a beautiful day, then we will go for a ride." Whereas the Law of Syllogism has two general statements that lead to a particular one.