How do Mendel's experiments show that traits are inherited independently ?

Explanation

Mendel performed dihybrid experiment on pea plants.
A tall plant with round seeds was crossed with a short plant with wrinkled seeds. `F_(1)` progeny plants were all tall with round seeds. `F_(1)` progeny are used to generate `F_(2)` progeny by self-pollination. Along with parental combinations, `F_(2)` progeny showed new combinations too. Some of them were tall with wrinkled seeds while some others were short with round seeds.
It means factors (genes) controlling for seed shape and height of plant recombine to form new combinations in `F_(2)` offsprings. Thus, tall/short trait and the round seed/wrinkled seeds trait are inherited independently.