How do Mendel's experiments show that the
(a) traits may be dominant or recessive,
(b) traits are inherited independently?

(a) When Mendel cross pollinated pure tall pea plants with pure dwarf pea plants, only tall plants were obtained in $F_1$ generation in 3:1 ratio. Thus appearence of tall character in both $F_1$ and $F_2$ shows that it is a dominant character. The absence of dwarf in $F_1$ generation reappears in $F_2$ shows dwarfness in the recessive character.
(b) When Mendel conducted a dihybrid cross having two sets of characters, he obtained only one set of parental characters in $F_1$ generation where as in $F_2$ generation he obtained both the set of parental characters as 9:3:3:1 ratio. Thus appearance of new generation or recombinants in the $F_2$ generation along with parental type shows that traits are inherited independently.