Problem $12.$ Which of the following statements about European option theta are correct? Select all that

apply.

a$.$ The $$ of $10\%$ out of the money option goes to minus infinity when time$-$to$-$maturity approaches zero

b$.$ The $$ of $10\%$ out of the money option goes to zero when time$-$to$-$maturity approaches zero

c$.$ The $$ can measure the loss of holding an at the money option as time goes by$.$

Please explain your answer.