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Premise 1: "All brown haired people are bad-tempered."
Premise 2 "My uncle has brown hair."
Conclusion: "Therefore, my uncle is bad-tempered."
you can see the above argument logically follows even though one of the premises is false.
Here's another example but one which does contain true premises but the argument is logically invalid:
Premise 1: Beer contains alcohol.
Premise 2: Wine contains alcohol.Conclusion: Therefore, Beer is Wine.