I thought that a laptop would cost a fortune; however, the prices have gone down considerably.
- Pensé que un notebook costaría una fortuna; sin embargo, los precios han caído considerablemente.
Tom thought where he put his gold coins was the perfect hiding place. However, he was wrong.
- Tom pensó que el lugar donde puso sus monedas de oro era el escondite perfecto. Sin embargo, estaba equivocado.
My cousin traveled to Spain two years ago, however my aunt has not yet heard from him.
- Mi primo viajó a España hace dos días, sin embargo aún no se ha comunicado con mi tía.
And yet, the contrary is always true as well.
- Y sin embargo, también lo contrario es siempre verdadero.