A syllogism is a logical argument in three parts.
the major premise eg all birds are have wings
the minor premise eg all eagles are birds
the conclusion eg all birds have wings
The major premise is a general statement believed to be true and the minor premise gives an example. If both premises are true, the conclusion may follow. If the reasoning is sound, the conclusion should follow from the two premises. . . .
A syllogism is valid when its conclusion follows from the premises. A syllogism is true when the premises are based on facts. To be sound, a syllogism must be both valid and true. However, a syllogism may be valid without being true or true without being valid.
A good example of a valid syllogism which is not true can be found by considering the work that can be done by workmen.
Major Premise: A man can build a bridge in a 800 minutes
Minor Premise: 800 men can work 800 times faster than one man
Conclusion: 800 men can build a bridge in 1 minute (an presumable the whole human race can build a bridge in the blink of an eye)
Obviously the conclusion is false. Both premises may be true though and if the conclusion had been, '800 men can build 800 bridges in 800 minutes' then they syllogism may have been true.