put option prices can be higher or lower the longer the time to expiration

I saw above in 2013 Mock but can’t seem to find a reference in books. Is above true for american or european

put option prices can be higher or lower the longer the time to expiration

I saw above in 2013 Mock but can’t seem to find a reference in books. Is above true for american or european

As time gets longer call options are higher, put options are lower.

Do the equation:

c + X/(1+rf)^t = p + S

It’s for European. This is due to the cost of carry benefit one can obtain by exercising a put option early (in an American option). Therefore that ‘lost’ in an European put option which is ITM may make it more expensive for options which are closer to maturity (exception to the general the longer the term, the more the time value, the more pricey).