If R is relation on a finite set A having n elements, then the number of reflexive relations on A is

a) 2ⁿ b) 2^{n^2-n} c) 𝑛² d) 𝑛ⁿ

^{Kindly answer with full explanation. Thank you}

The function 𝑓:𝑅→𝑅 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑏𝑦 𝑓(𝑥)=2^x+2^|x| is
a) one-one and onto   b) many-one and onto
c) one-one and into    d) many-one and into

Please give full explanation. Thank you

If A and B have 𝑚 𝑎𝑛𝑑 𝑛 elements respectively, then the number of possible functions from A to B is

a) 𝑛𝑚   b) 𝑚𝑛   c) 𝑚𝑛
d) 𝑚+𝑛

𝐼𝑓 𝑓(𝑥)=2𝑥−1/𝑥+2, then 𝑓(1)𝑓^-1(−1)=
 

a) 0    b) 1    c) -1    d) 2

If 𝑓(𝑥) is a function such that 𝑓(𝑥+𝑦)=𝑓(𝑥) 𝑓(𝑦) 𝑎𝑛𝑑 𝑓(3)=125 𝑡ℎ𝑒𝑛 𝑓(𝑥)=
a) 5    b) 𝑥⁵  c) 5𝑥 d) 5^x

^{Please give full explanation. Thank you}

The function 𝑓:𝑅→𝑅 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑏𝑦 𝑓(𝑥)=2𝑥+2|𝑥| is
a) one-one and onto   b) many-one and onto
c) one-one and into    d) many-one and into

Please give full explanation. Thank you