Problem $6($Calculation with Lambda Expressions$).$ For each of the following, write a lambda

expression to calculate the function. You can use any of the functions I covered in class or in the slides,

but you should not use recursion for any of the functions. For all questions the functions are for

numbers represented as Church numerals.

a$.$ ONETRUE $=(!$a$.!$b$.!$c$.......)$ should calculate ONETRUE a b c defined as follows

$1.$ ONETRU fls fls fls $=$ fls

$2.$ ONETRU fls fls tru $=$ tru

$3.$ ONETRU fls tru fls $=$ tru

$4.$ ONETRU fls tru tru $=$ fls

$5.$ ONETRU tru fls fls $=$ tru

$6.$ ONETRU tru fls tru $=$ fls

$7.$ ONETRU tru tru fls $=$ fls

$8.$ ONETRU tru tru tru $=$ fls

b$.$ sum$\_$products $=(!$n$.......)$ should calculate $1*2+3*4+5*6+$ n$*($n$+1)$

c$.$ DIV$3=$ integer division by $3.$

Examples DIV$32=0$

DIV$35=1$

MOD$36=2$

MOD$37=2$

e$.($Bonus$)$ Can you generalize this for integer division by n$?$