a) Mendel performs a monohybrid cross to prove that traits can be either dominant or recessive. He crossed two homozygous pure varieties tall (TT) and dwarf (tt) pea plants.  The offsprings in the first generation (F1) were all tall and there were no dwarf plants. When these F1 plants were fertilized by their own pollen (selfed), the offsprings of the second generation (F2) were both tall and dwarf. About three-fourths of the plants were tall and one-fourth were dwarf. This showed that the character of dwarfness which disappeared in the F1 generation reappeared in the F2 generation.  Thus, Mendel concluded that of the two alleles for a trait, one is dominant and other is recessive. The parental character which is expressed in F1 is the dominant character controlled by a dominant allele (TT) and the character of the other parent which is not expressed is referred as recessive, controlled by a recessive allele (tt). Thus, the recessive trait is unable to express in the heterozygous condition (F1 generation) while able to express in homozygous condition (F2 generation). This experiment depicts that the traits can be dominant or recessive.  b) Mendel carried out a dihybrid cross to demonstrate that inheritance of two traits is independent of each other. Mendel considered two pure varieties one with yellow cotyledon (YY), round seed (RR) and another with green cotyledon (yy), wrinkled seed (rr). From the cross between two parental generation plants, the offsprings in the F1 generation were all with yellow cotyledon and round seed. When these F1 plants were self-fertilized, the offsprings of $$F_2$$ generation were of four types in the ratio 9:3:3:1 - 1) yellow cotyledon, round seed 2) yellow cotyledon, wrinkled seed 3) green cotyledon, round seed 4) green cotyledon, wrinkled seed.  This shows that two pairs of character or traits behave independently of each other. Each pair of contrasting bears no permanent association with a particular character.