conditional identities

Conditional Trigonometric Identities - In the previous sections many identities have been discussed. They are true for all values of the angles for which trigonometric functions are defined. In this section we prove identities, where a certain relationship ex..

In the previous sections many identities have been discussed. They are true for all values of the angles for which trigonometric functions are defined. In this section we prove identities, where a certain relationship exists among the angles considered. Many interesting and impo..

Crystals are solid particles bounded by plane surfaces, which make definite angles with each other. This gives a definite geometrical shape to the crystal. These shapes are different for different crystals (Fig.6.13). Crystals of the same substance are identical only under iden..

Variation - Variation may be defined as differences among individuals of a species. All around us we see different organisms belonging to different species. Within each species too, no two individuals are identical to each other. Asexual reproduction produces identical offspring..

The monozygotic (identical twins) develop from a single zygote by separation of the two blastomeres after the first cleavage. Therefore, they have similar genetic traits, except for rare chances of mutation. Fraternal twins develop from different zygotes. Therefore, they are no more alike..

Crystallisation - Crystals are solid particles bounded by plane surfaces, which make definite angles with each other. This gives a definite geometrical shape to the crystal. These shapes are different for different crystals (Fig.6.13). Crystals of the same substance are identical only und..

The offsprings are genetically identical and therefore advantageous traits can be preserved. Only one parent is required which eliminates the need for special mechanisms such as pollination, etc. It is faster. For example, bacteria can multiply every 20 minutes. This helps the organis..

The offsprings are genetically identical and therefore advantageous traits can be preserved. Only one parent is required which eliminates the need for special mechanisms such as pollination, etc. It is faster. For example, bacteria can multiply every 20 minutes. This helps the org..

Mitosis becomes significant for the following reasons. Mitosis forms two daughter cells which will have the same chromosome number and same genetic material as the parent cell. Daughter cells formed from mitosis are genetically identical to their parent cell and no variation would be intr..

If p and q are propositions, then the conjunction of conditionals p q and q p is called a biconditional proposition. Let us construct the truth table of (p q) (q p) The last column of above table is identical to the last column of earlier table..