Rendirse vs. darse por vencido vs. tirar la toalla

In Spanish, there are several phrases that convey the idea of giving up or admitting defeat. These include 'rendirse', 'darse por vencido', and 'tirar la toalla'. Each expression has its unique nuances and contexts where it is commonly used.

Rendirse

The verb 'rendirse' means to surrender or to give up. It often implies conceding in a battle, competition, or challenge.
Después de luchar durante horas, el ejército decidió rendirse.
(After fighting for hours, the army decided to surrender.)
No me voy a rendir hasta lograr mi objetivo.
(I am not going to give up until I achieve my goal.)

Darse por vencido

'Darse por vencido' translates to considering oneself defeated or giving up. It is usually used when someone decides they cannot win.
Aunque fallé varias veces, no me doy por vencido.
(Even though I failed several times, I do not give up.)
Se dio por vencido después de intentar resolver el problema toda la noche.
(He gave up after trying to solve the problem all night.)

Tirar la toalla

'Tirar la toalla' is an idiomatic expression meaning to throw in the towel. It originates from boxing, where throwing a towel indicates surrender.
Después de varios intentos fallidos, finalmente tiró la toalla.
(After several failed attempts, he finally threw in the towel.)
No podemos tirar la toalla ahora; estamos muy cerca de lograrlo.
(We can't throw in the towel now; we're very close to achieving it.)

Summary

'Rendirse', 'darse por vencido', and 'tirar la toalla' all express the notion of giving up but in slightly different ways. 'Rendirse' is more formal and often used in the literal sense of surrendering. 'Darse por vencido' focuses on internal defeat or acceptance of failure. 'Tirar la toalla' is colloquial and metaphorical, borrowing from boxing terminology.