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 Sorry sir i have typed it wrong. The question was -

What is the meaning of the set - E={x:x ∈ 1 and -1}?

Given,

E={x : x ∈ 1 and -1}

We never use '∈' sign for any given number. It is used for representing the set of numbers like natural numbers, real numbers, integers etc. 

As per the query mentioned by you, the conclusion which can be drawn as:

x = {1, -1}  

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You have prob­a­bly heard about cog­ni­tive abil­i­ties or cog­ni­tion. What is cog­ni­tion? Cog­ni­tion has to do with how a per­son under­stands and acts in the world. It is a set of abil­i­ties, skills or processes that are part of nearly every human action.

Cog­ni­tive abil­i­ties are the brain-based skills we need to carry out any task from the sim­plest to the most com­plex. They have more to do with the mech­a­nisms of how we learn, remem­ber, problem-solve, and pay atten­tion rather than with any actual knowl­edge. Any task can be bro­ken down into the dif­fer­ent cog­ni­tive skills or func­tions needed to com­plete that task suc­cess­fully. For instance, answer­ing the tele­phone involves at least: per­cep­tion (hear­ing the ring tone), deci­sion tak­ing (answer­ing or not), motor skill (lift­ing the receiver), lan­guage skills (talk­ing and under­stand­ing lan­guage), social skills (inter­pret­ing tone of voice and inter­act­ing prop­erly with another human being).

The fields of neu­ropsy­chol­ogy, cog­ni­tive psy­chol­ogy, and thus cog­ni­tive train­ing are based on the frame­work that cog­ni­tion con­sists of dif­fer­ent men­tal func­tions or cog­ni­tive abil­i­ties which are based on spe­cific con­stel­la­tions of brain struc­tures. For instance mem­ory skills rely mainly on parts of the tem­po­ral lobes (next to the tem­ples) and parts of the frontal lobes (behind the forehead).

In the table below, you can browse through the main brain func­tions involved in cog­ni­tion. You will also find brain teasers that will help you chal­lenge all the cog­ni­tive abil­i­ties described: Learn and have fun!

COGNITIVE ABILITIES ARE MENTAL SKILLS

Cog­ni­tive Ability/Brain Func­tion
 Skills involved
Per­cep­tion

Recog­ni­tion and inter­pre­ta­tion of sen­sory stim­uli (smell, touch, hear­ing, etc.)

Brain chal­lenges:
Atten­tion Abil­ity to sus­tain con­cen­tra­tion on a par­tic­u­lar object, action, or thought.
Abil­ity to man­age com­pet­ing demands in our environment.Brain challenges:
Mem­ory Short-term/ work­ing mem­ory (lim­ited stor­age).
Long-term mem­ory (unlim­ited storage).Brain challenges:
Motor Abil­ity to mobi­lize our mus­cles and bod­ies.
Abil­ity to manip­u­late objects.

Brain chal­lenges:

  • Tap your right hand on the table. At the same time, make a cir­cu­lar move­ment with  your left hand (as if you were clean­ing the table)
  • Switch hands
Lan­guage Skills allow­ing us to trans­late sounds into words and gen­er­ate ver­bal output.

Brain chal­lenges:
Visual and Spa­tial Processing Abil­ity to process incom­ing visual stimuli.Ability to under­stand spa­tial rela­tion­ship between objects.

Abil­ity to visu­al­ize images and scenarios.

Brain chal­lenges:
Exec­u­tive Functions Abil­i­ties that enable goal-oriented behav­ior, such as the abil­ity to plan, and exe­cute a goal. These include:
Flex­i­bil­ity: the capac­ity for quickly switch­ing to the appro­pri­ate men­tal mode.

The­ory of mind: insight into other people’s inner world, their plans, their likes and dis­likes.

Antic­i­pa­tion: pre­dic­tion based on pat­tern recog­ni­tion.

Problem-solving: defin­ing the prob­lem in the right way to then gen­er­ate solu­tions and pick the right one.

Deci­sion mak­ing: the abil­ity to make deci­sions based on problem-solving, on incom­plete infor­ma­tion and on emo­tions (ours and oth­ers’).

Work­ing Mem­ory: the capac­ity to hold and manip­u­late infor­ma­tion “on-line” in real time.

Emo­tional self-regulation: the abil­ity to iden­tify and man­age one’s own emo­tions for good per­for­mance.

Sequenc­ing: the abil­ity to break down com­plex actions into man­age­able units and pri­or­i­tize them in the right order.

Inhi­bi­tion: the abil­ity to with­stand dis­trac­tion, and inter­nal urges.

Brain chal­lenges:

.

COGNITIVE ABILITIES CAN IMPROVE IF EXERCISED

With age, some cog­ni­tive abil­i­ties decline, espe­cially the exec­u­tive func­tions. In addi­tion, cog­ni­tive abil­i­ties that are not used reg­u­larly tend to dimin­ish over time. This may hap­pen at any age but is mostly observed in older age. For­tu­nately, these skills can also be improved at any age with reg­u­lar practice.

Fur­ther rel­e­vant and use­ful resources:

- An inter­view with Yaakov Stern, explain­ing what cog­ni­tive reserve is and how cog­ni­tive abil­i­ties can be improved through life­time experiences.

- Short posts on what can boost cog­ni­tive abilities:

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